# Suppose The Length And Width Of The Box In Exercise 12 Double. Does The Surface Area S Double? Explain (2023)

Mathematics Middle School

No, it does not.

In general, surface area is the sum of the areas of each face of a prism. In a rectangular prism, we have length, width, and height.

The area of the bottom of the prism and the top of the prism is the same, and can be represented as l*w. This means that together, it is 2lw.

The area of the left and right faces of the prism is the same, and can be represented as l*h. This means that together, it is 2lh.

The area of the front and back faces of the prism is the same, and can be represented as w*h. This means that together, it is 2wh.

This gives us the equation

SA = 2lw+2lh+2wh

If we double the length and width, making them each 2l, we then have:

SA = 2(2l*2w) + 2(2l*h) + 2(2w*h)
= 2(4lw) + 4lh + 4wh
= 8lw + 4lh + 4wh

If the surface area had been doubled, we would expect
4lw + 4lh + 4wh

No, it is not doubled.

## Related Questions

jorge is playing football. he carries the ball forward 5 2/3 yards and then moves backward 1 foot. how far forward is the ball, in feet, from where jorge started carrying the ball?

The ball is 16 feet forward from where Jorge started carrying it.

What is Unit of Measurement?

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that Jorge carries the ball forward yards and then moves backward 1 foot.

We need to find how far the ball.

Lets convert yards to feet:

yards = 5 + 2/3 yards

= (5×3 feet/yard) + (2/3 × 3 feet/yard)

= 15 + 2 feet

= 17 feet

So, Jorge moved the ball forward 17 feet.

Then, he moved the ball backward 1 foot, so the ball is now 17 - 1 = 16 feet from where he started carrying it.

Hence, the ball is 16 feet forward from where Jorge started carrying it.

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Lets convert yards to feet. There are 3 feet in a yard.
5 2/3 x 3 = 17 feet

Jorge carried the ball 17 ft forward, then 1 ft backwards
17-1=16

The ball is 16 ft in front of where it started
(Also the same as 15 1/3 yards)

Start time 3:20 pm end time 6:00 pm what is the elapsed time

2 hours and 40 minutes :)

2 hours and 40 minutes and hope it helps
And can you mark brainliest please I help

What is the Mean absolute value of 10,16,18,15,15,10,23

15.3 you add all of them together then divide by the quantity of numbers

Which is greater 17 qt or 4 gal ??

17 quarts = 4.25 Gallons

17qts

hope this helped

THe temperature is negative 7 degrees and overnight it gets 12 degrees warmer? Then during the day it gets 12 degrees warmer?

At the start the temperature is -7 overnight it gets 12 degrees warmer so -7+12 =5 degrees than during the day it gets 12 degrees warmer so 5+12= 17 degrees

During his summer vacation, Alex spent 6 minutes riding his bike for every minute he spent watching television. If he rode his bike for 750 minutes, how many minutes did he spend watching television?

4500 minutes, or 75 hours

(-4z=20) i got 16 by dividing 20 by negative 4 and getting z=16

-4z= 20
to get z alone, divide both sides by -4

-4z/-4= 20/-4

-4 on the left cancels out; divide 20 by -4

the answer will also be negative since 20 is positive and you need two negatives to make a positive

z= -5

CHECK:
(-4)(-5)= 20
20= 20

Hope this helps! :)

-4z/-4=20/-4
z=-5
by dividing you should get -5

The volume of a cube shaped box is 27 cubic centimeters . What is the height of the box

V(cube)=a³=27
a=3
height =3cm

Hi there!

A cube basically has same length, width, and height.
So if the length is 2, then the width and height has to be 2.

To find a volume of a cube, you would have to multiply length× width× height.
Since the length, width, and height are all same, you can write the formula as

V = x³
(x is the length, width, and height!)

You would have to multiply same number three times in order to get 27.
∛27 = 3.
3× 3× 3 = 27.
So you know that your length, width, and height is 3cm!

The height of the box is 3cm.

Hope this helped!! :)

jeff wants to buy a phone card for long distance calls. he can buy a 200-minute card for \$10.00 or a 300-minute card for \$12.00. which card is the better value

200 min / \$10.00 = 20 minutes / dollar

300 min / \$12.00 = 25 minutes / dollar

The cost of the 300 minute card is cheaper per minute and a better value.

If you don't expect to use more than 200 minutes then save your money and buy the smaller card.

300 Minute card.

It's 20 mins per \$1 for the \$10 plan. using the same pricing you would only get 240 mins for \$12. So 300 for \$12 is the better deal.

What is 5-6x=2+7x step by step?

The first thing you do is subtract 2 from both sides to move the 2 to the left side
3-6x=7x
now add 6x to both sides to move -6x to the right
3=13x
divide by 13 to eliminate the 13 on the right side
3/13

5-6x=2+7x
subtract 2 on both sides which would look like
5-6x= 2+7x
-2 =-2
so you will get
3-6x=7x
now you add 6x on both sides
3-6x= 7x
+6x=+6x
so now you would get
3=13x
so now you divide 13 on both sides
3=13x
/13=/13
x=3/13 or as a decimal x=0.230769

hope this helped

Luka wants to know the theoretical and experimental probability of rolling a number smaller than a 5 on a 6-sided number cube numbered 1 to 6. He rolls the number cube 10 times and records the results in this table. 15264 62563 Drag and drop the answers in the boxes to correctly complete the sentences comparing theoretical probability and experimental probability. actually happenedwe expect to happen231216 The theoretical probability of rolling a number smaller than 5 is because this is what . The experimental probability of rolling a number smaller than 5 is because this is what .

The experimental probability is the probability that’s we obtain from an experiment (from trials) here rolling the die and noting the number. Luka rolled ten times and 5 of these yielded a number less than 5 (the numbers on a 6-sided die that areless than five are 1, 2, 3, 4). So there were 5 out of 10 times that a number rolled was less than 5. This makes the experimental probability 5/10.

The theoretical probability is obtained through mathematical thinking (not by trying it an keeping track). On a 6-sided die there are 4 numbers less than 5. There are 6 numbers in all. Every number is equally likely to appear so the probability that a number rolled is less than 5 is 4/6. This is the theoretical probability.

As an aside, the more times you roll (100, 1000, 1000000 rolls) the closer the experimental probability (what you observe) gets to the theoretical probability (what you would expect by reasoning it out mathematically).

2/3

we expect to happen

1/2

actually happend

Start time 3:30 pm end time 7:00 pm what is elapsed time?

The solution is, the value of elapsed time = 3 hours 30 mint.

What is Subtraction?

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

given that,

start time 3:30 pm

end time 7:00 pm

now, we have to find the elapsed time.

we know that,

to get elapsed time,

we have,

elapsed time = end time - start time

i.e. elapsed time = 7:00 pm - 3:30 pm

now, we have,

6 hours - 3 hours = 3 hours

and, 60 mint. - 30 mint. = 30 mint.

as, 7:00 pm = 7 hours

= 6: 60

= 6 hours. + 60 mint

and, 3:30 pm = 3 hours + 30 mints.

so, we get,

elapsed time = 7:00 pm - 3:30 pm

= 3 hours 30 mint.

Hence, The solution is, the value of elapsed time = 3 hours 30 mint.

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Hello there!

I hope I have been of assistance!

~ Fire

Start time 8:10 end time10:55 what is the elapsed time?

2 hours and 45 minutes should be the answer. Hope I helped :)

The elapsed time is 2 hours and 45 minutes.You subtract the 8 from the 10, leaving 2 hours.You subtract the 10 from the 55, leaving 45 minutes.

john eats a bowl of cereal for 3 of his 4 meals each day. He finishes two gallons of milk in eight days . How much milk does john use for one bowl of cereal?

He has 24 meals that use milk in 8 days. If he finished 2 gallons in 24 sittings, he uses 2/24 of a gallon a day which simplifies to 1/12 gallon a day.

He uses 0.0833333 gallons/ 303 ml for each meal

An investment made in the stock market decreased at a rate of 1.2% per year for 25 years. What is the current value of the \$100,000 investment? Include your calculations in your final answer.

The formula used is A = P (1 + r/n) ^(nt). Because of the negative interest, the compounded amount is only \$695,929.30.

What is 2+5x=7-3x equal step by step

Step 1:
Move the 3x to the leftbside by adding 3x to both -3x snd 5x. So you now have 2+2x=7

Step 2:
subtrac2 3 from both 7 and 2, so you know have 2x=5.

Step 3:
divide 2x and 5 by 2. You noe have the answer: x=2.5

Set the x’s equal to each other, so move them to the same side.
2+5x+3x=7
Now move the 2 over to set it equal to 7.
5x+3x=7-2
5x+3x=8x
7-2=5
8x=5.
Divide to make the X stand alone to find the answer. x=5/8.

Which expression is equivalent to 1/4(2−5x+6) ? A −5/4x+1
B −5/4x=2
C −5x+6 1/2
D −5x+8

Hello there.

Which expression is equivalent to 1/4(2−5x+6) ?

a Christian University found that about 3% of its students came from certain state the university had 156 students from that state what is the total enrollment in the University

The total enrollment of student in the University equals to 5,200 students.

How do we calculate the total enrollment in the University?

We will use the limited data to calculate the total enrollment of students in the University.

• Now, we will use the following ratio to solve:

156/x = 3/100

Now, we do cross multiplication

156 * 100 = 3x

x = 5200

Therefore, the total enrollment of student in the University equals to 5,200 students.

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Do a ratio

156/x = 3/100

then cross multiply

156 * 100 = 3x

x = 5200

What is 1+1? (hard question) BONUS (to get brainliest) - Why is building a wall good to make America Great Again?

2....... and just because we can thats why

like look at china they built one after all ;P

1 +1=2 I had to think really hard in this question :,)

How do you find the rate of change of a table

Change in y over change in x

Y over x is the answer

## FAQs

### What happens to surface area when length is doubled? ›

. Doubling the dimensions makes the surface area 4 times the original surface area. Tripling the dimensions makes the surface area 9 times the original surface area.

How does doubling both the length and width of a rectangle affect its area? ›

Comparing ( 1 ) and ( 2 ) we can see, ⇒ If the length and the breadth of a rectangle are doubled then its area becomes 4 times.

What happens to the surface area of a rectangular prism when each length is doubled? ›

Therefore, doubling the dimensions of a rectangular prism increases the surface area of the prism by a factor of 4.

What happens when the length is doubled? ›

Hence, if the length of a wire is doubled, then its resistance becomes doubled.

Does surface area increase or decrease? ›

Explanation: Increasing the surface area increases the rate of the reaction because there'll be more number of reactant molecules exposed for the reaction . This translates to an increase in number of successful collisions per unit time . Thus, higher reaction rate.

What happens when the longer side of the rectangle is doubled and the other reduce to half? ›

Hence, there is no change in the area of the rectangle.

Does doubling the side length of a square double the area? ›

No worries!

How much would the area increase if the length and width of a square were doubled? ›

area of the square increases 4 times.

What happens to the volume of a rectangular prism when the dimensions are doubled? ›

If its length, width, and height is doubled, then its volume will be (2l) × (2w) × (2h) = 8lwh = 8 × v. Thus, we can conclude that if its length, width, and height is doubled, the volume of the rectangular prism will be 8 times the original value.

When the length of a square is doubled its area will increase? ›

Therefore, side of the square is doubled then the area of the square obtained is 4 times the old area.

### What happens to the surface area if the edge length of a cube is doubled? ›

Hence, surface area will increase 4 times.

How do you find the surface area with the length and width? ›

Or, you can label the length (l), width (w), and height (h) of the cuboid and use the formula: surface area (SA)=2lw+2lh+2hw.

What is the formula for Lxwxh? ›

Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.

Why is area halved when length is doubled? ›

As the length of wire gets doubled, the cross-sectional area will become half of its previous value because volume of wire remains constant.

What happens when the length of a rectangle is doubled without changing the width? ›

when the length is doubled of a rectangle and breadth remains same the area becomes doubled. and if breadth is double and length remains same the area becomes doubled.

How are the area and volume each affected if the side length is doubled? ›

If the side length is doubled, the area is quadrupled and the volume is multiplied by 8. If the side length is tripled, the area is multiplied by 9 and the volume is multiplied by 27.

Does surface area increase as size increases? ›

As a cell grows in size, the surface area gets bigger, but the volume gets bigger faster.

What happens when you increase surface area? ›

Increasing the surface area of a reactant increases the frequency of collisions and increases the reaction rate. Several smaller particles have more surface area than one large particle. The more surface area that is available for particles to collide, the faster the reaction will occur.

Why does surface area increase with decrease in size? ›

It also means that when a given volume of material is made up of smaller particles, the surface area of the material increases. Therefore, as particle size decreases, a greater proportion of the particles are found at the surface of the material.

What is the increase in area when the sides of a rectangle are increased in length by 100%? ›

% of increase in area of rectangle=xy3xy×100=300%

### What will happen to the area of a square if its side is increased by half? ›

(ii) Increased by half of it. Hence, the area becomes 9 times more than that of the original area.

How does doubling the side lengths of a triangle affect its area? ›

Hence, if each side of a triangle is doubled, then its area is 4 times the area of the original triangle.

What effect does doubling the side length of a cube have on its surface area to volume ratio? ›

All together then, when we double the side length of a cube, its volume increases by a factor of eight and its surface area grows by a factor of four.

How do you double the area of a square? ›

Doubling the Area of a Given Square. Why it works: The area of the original square is AB^2, so we want a square of area 2AB^2. If the side of the new square is s, then we want s^2 = 2AB^2, or s = AB*sqrt(2), which is the length of the diagonal of the square.

Does the surface area double if you double the height of a right prism? ›

If the dimensions of the rectangular prism are doubled, the surface area will increase 4 times.

What happens to the perimeter of a rectangle when you double the length and width? ›

Hence, the perimeter of a rectangle becomes two times its original perimeter if its length and breadth are doubled.

What is the increase in the side of a square if the area of the square is increased by 69? ›

So, length is increased by 30%

What is the increase in the area if the figure is a square and the sides are increased by 20% each? ›

percentage increase in are =44%

What factor is the volume increased if the length and width are doubled? ›

If you double just two dimensions (x, y) the volume will increase by a factor of four. IE.

How many times will volume increase if the dimensions of a cube are doubled? ›

Hence volume will increase 7 times.

### What happens to the volume of a cube if the length is doubled? ›

thus the volume becomes 8 times the original volume.

What will be the change in area of a rectangle if its length is increased by 15% and no change in the breadth? ›

∴ The required result will be 5.8% increase.

What will be the area of a square increases by _____ if its side increases by 30%? ›

∴ The area is increased by 69%.

Does the area of a square increases if we increase the length of its sides are the two quantities in direct proportion? ›

This statement is False. Explanation: Length of a side of a square and its area does not vary directly with each other, e.g. Let a be length of each side of a square. So, if we increase the length of the side of a square, then their area increases but not directly.

What happens to the volume of a cube if the length of its edge becomes half? ›

Hence, if the edge of the cube is halved, then the volume becomes 18 times.

What is the surface area of a rectangle if the length is 5cm and the width is 3cm? ›

Hence, Area of rectangle with length 5 cm and breadth 3 cm is 15 cm2.

How does the total surface area of a box change if each dimension is doubled? ›

Thus the total surface area is increased to four times when the side is doubled.

How to calculate surface area? ›

What is surface area? The surface area of a three dimensional shape is the total area of all of the faces. To find the surface area of a shape, we find the area of each face and add them together.

How do you measure Lxwxh on a box? ›

Measure the length of the box first. This is the long side of the box on the side of the longest flap. Next, turn the box 90 degrees and measure the width, which is the side with the shorter flap. Last, measure the height of the package.

What does Lxwxh mean in math? ›

Length x Width x Height.

### What happens to area when length increases? ›

If a wire is stretched, then the length of the wire increases and area also decreases.

What is the relationship between surface area and length? ›

Surface area = length x length (or length2) multiplied by the number of sides (6).

What happens to the surface area as the size increases? ›

As a cell grows in size, the surface area gets bigger, but the volume gets bigger faster.

Does size affect surface area? ›

As the radius of a cell increases, its surface area increases as the square of its radius, but its volume increases as the cube of its radius (much more rapidly). Therefore, as a cell increases in size, its surface area-to-volume ratio decreases.

What is the relationship between the length of a side and the surface area to volume ratio of a cell? ›

As cells increase in size, the surface area and volume do not usually increase proportionally to length. The greater the diameter of a single-celled organism, the lower the surface area to volume ratio. It is this relationship that restricts the size of a particular cell.

What is the relationship between the area of a square and the length of one side? ›

And that is that the area of a square is equal to the length times the length, or the length squared.

What happens to the surface area and volume as the size increases? ›

As a cell becomes larger, its surface area increases more slowly than its volume. That is, the surface area to volume ratio decreases, as the denominator of the ratio grows more quickly than the numerator.

How many times does the volume and surface area increase if the length of a cube is doubled? ›

Hence, Volume is increased 8 times and the surface area is 4 times.

What happens to the volume of a sphere if the radius is doubled? ›

How many times area is changed when the sides are doubled? ›

Hence, if each side of a triangle is doubled, then its area is 4 times the area of the original triangle. Q.

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