Question

2. A prism has total surface area of 158 m2 and volume of 120 m3.
If the length, width, and height are reduced to one third their original sizes, what will be the following? Round to tenths if necessary.
(a) the new surface area
The new surface area is

(b) the new volume
The new volume is

If the length, width, and height of the original are increased to quadruple their original sizes, what will be the following?
(c) the new surface area


(d) the new volume

Answer 1

someone help please im fairly new here

Answer 2

@TheSmartOne

Answer 3

When you change the linear dimensions (length, width, height, radius, etc.) of a solid by a factor of \(k\), the surface area changes by a factor of \(k^2\), and the volume changes by a factor of \(k^3\).

Answer 4

Ok but im not understanding how to get the new surface area or the new volume. @mathstudent55

Answer 5

it says it reduced to 1/3 but i dont understand how to get the new surface area or volume. ive been stuck on this for days now. its stressful. i just need to get it out of the way.

Answer 6

Someone help me understand?

Answer 7

Since the surface area is base*width, If you third each dimension you get 1/3b*1/3w or 1/9bw. Since bw=158, just plug that in and you get 1/3*158.
Since the volume is base*width*hieght, if you third each dimension you get 13b*1/3w*1/3h or 1/27bwh. Since bwd=120, just plug that in and you get 1/27*120.

Answer 8

Since the surface area is base*width, If you quadruple each dimension you get 4b*4w or 16bw. Since bw=158, just plug that in and you get 16*158.

Since the volume is base*width*hieght, if you quadruple each dimension you get 4b*4w*4h or 64bwh. Since bwd=120, just plug that in and you get 64*120.

Answer 9

Here is an example to make it easier to understand.
Start with a solid with a given surface area and a given volume.
Let's say you start with a cube with surface area 24 m^2 and volume 8 m^3.
If every edge (length, width, height) becomes 3 times as long, then the surface area becomes 3^2 = 9 times as large, the the volume becomes 3^3 = 27 times as large.
The new surface area would now be 24 * 9 m^2 and the new volume would be 8 * 27 m^3.

Answer 10

In your case, the dimensions became 1/3 if what they were.
The length is now 1/3 of what it was.
The width is now 1/3 of what it was.
The height is now 1/3 of what it was.

If you square the change, (1/3)^2 = 1/9, that tells you what the surface area becomes. It is now 1/9 of what it was.
If you cube the change, (1/3)^3 = 1/27, it tells you what the new volume is now. It is 1/27 of the original volume.

Answer 11

The new area is 1/9 of 158 m^2, and the new volume is 1/27 of 120 m^3.

Answer 12

Do you understand it now?

Answer 13

yes perfectly. It made everything else easier also. thank you for explaining that for me. That was appreciated.

Answer 14

but then this part??
If the length, width, and height of the original are increased to quadruple their original sizes, what will be the following?

Answer 15

@mathstudent55

Answer 16

Since the surface area is base*width, If you quadruple each dimension you get 4b*4w or 16bw. Since bw=158, just plug that in and you get 16*158.

Since the volume is base*width*hieght, if you quadruple each dimension you get 4b*4w*4h or 64bwh. Since bwd=120, just plug that in and you get 64*120.

Answer 17

so for the first part the new surface area is 1/9 m^2? and the new volume is 1/27 m^3 ??

Answer 18

I apologize i may be still confused lol

Answer 19

@bmk614

Answer 20

For part a) the new surface area is one-ninth the original area. You need to divide the old area by 9. What is 158 m^2 divided by 9?

For part b), the new volume is found by dividing the old volume by 27, since the new smaller volume is 1/27 of the old volume. What is 120 m^2 divided by 27?

For part c), the new solid has linear dimensions that are 4 times the original dimensions, so the new area is 4^2 = 16 times the original area. The new area is now 16 * 158 m^2.

For part d), the new volume is 4^3 = 64 times the original volume. Since the original volume is 120 m^3, the new volume is 64 * 120 m^3

Answer 21

For a) 1/9 is what you multiply the original area to find the new area. That means divide the original area by 9.
For b) 1/27 is what you multiply the original volume to find the new volume. That means divide the original volume by 27.
For part c) multiply the original area by 16.
For part d) multiply the original volume by 64.

Answer 22

Is it clearer now?

Answer 23

So it would be 18m^2 and 4m^3 for the first part of the question?

Answer 24

@mathstudent55

Answer 25

or would the new volume be 0.225 and then rounded?

Answer 26

oh, 0.225 doesnt make sense anyway i dont think. Thanks for your help !!!