Question

2. A prism has total surface area of 360 m^2 and volume of 60 m^3.
If the length, width, and height are reduced to half their original sizes, what will be the following?
a.) the new surface area
b.) the new volume
If the length, width, and height of the original are increased to triple their original sizes, what will be the following?
c.) the new surface area
d.) the new volume
Show your calculations for all four parts.

Answer 1

A prism has total surface area of 360 m^2.

the length, width, and height are reduced to half their original sizes, what will be the new surface area?
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Theorem Needed:

If two solids are similar, the square of the scale factor of the two solids is equal to the ratio of any two corresponding area measurements of the solids.

Answer 2

oh okay

Answer 3

1440?

Answer 4

1440? I don't think so. The formula is upside down.

Answer 5

60 over V = 1 over 8?

Answer 6

The values should be getting smaller.

Back to surface area.

sing the theorem, the old surface area is to the new surface area as the square of the scale factor.

360/x = (2/1)^2 The original has dimensions twice the second one.

360/x = 4/1

Cross multiply and solve for x.

Now, what is this?

Answer 7

90?

Answer 8

That is what I got.

Answer 9

Now to volume.

Answer 10

60/V = (2/1)^3
60/V = 8/1
Cross multiply and solve for V.

Answer 11

Answer?

Answer 12

7.5

Answer 13

60/8 = 7.5 cubic meters

Answer 14

so my answer was wrong?

Answer 15

I thought we got the same thing. 7.5

Answer 16

Part II:

Here are the two theorems we are using:

If two solids are similar, the cube of the scale factor of the two solids is equal to the ratio of the volumes.
　
If two solids are similar, the square of the scale factor of the two solids is equal to the ratio of any two corresponding area measurements of the solids.

Answer 17

no i was just making sure xD

Answer 18

sorry xd moving on

Answer 19

Okay.

This time the original solid has its dimensions tripled.
The scale factor from small to large is 1 to 3.

360/S = (1/3)^2 where S is the surface area of the larger solid

Answer 20

9720?

Answer 21

I messed up again. 1/3 times 1/3 = 1/9, not 1/27.

Answer 22

360/S = 1/9

Cross multiply and solve for S.

Answer 23

3240?

Answer 24

3240 square meters is what I got.
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60/V = (1/3)^3 where V is the volume of the larger solid.

60/V = 1/27

Cross multiply and solve for V.

Answer 25

1620

Answer 26

That's what I got.

Answer 27

so that's all ?

Answer 28

k last question

Answer 29

Put it in a new thread.

Answer 30

Oh, that was the last question. I thought you were saying that there is another.

Answer 31

there is i just asked it