Question

This prism has a volume of 90 cm3.

What would the volume of the prism be if each dimension was tripled? (Scale factor is 3.)



A.
2700 cm3

B.
270 cm3

C.
2430 cm3

D.
810 cm3

Answer 1

http://static.k12.com/calms_media/media/395500_396000/395701/2/7bd91c39fae98f0bb3311ba8522b37272b1e0aad/53251_question.jpg

Answer 2

@mathstudent55

Answer 3

You can solve this 2 different ways.

Answer 4

I will explain both ways to you.

Answer 5

if each dimension is * 3 then volume is * 3^3

Answer 6

wait the answer is 270 right

Answer 7

We saw earlier (the microwave oven problem) that the volume of a rectangular prism is:
V = LWH

Answer 8

is it 270

Answer 9

We can check this problem.
The dimensions are 6 cm, 5 cm, 3 cm.
We multiply them all together, and we get V = 6 cm * 5 cm * 3 cm = 90 cm^3
That is what the problem tells us the original volume is.

Answer 10

k

Answer 11

The answer is not 270. We'll get there soon.

Answer 12

ok

Answer 13

The problem tells us each measure is multiplied by 3.
Now let's multiply each measure by 3 and find the volume again.

Answer 14

k

Answer 15

6 cm * 3 = 18 cm
5 cm * 3 = 15 cm
3 cm * 3 = 9 cm
Now we find the volume using our new dimensions that are 3 times larger than the original dimensions:
V = 18 cm * 15 cm * 9 cm =

Answer 16

What do you get?

Answer 17

all of it i think the answer is 2430

Answer 18

Correct. Remember it's with cm^3 units.

Answer 19

That was the first way of solving the problem.
Here is the second way.

Answer 20

k here is a medal im going to post up another question

Answer 21

If you have a solid and you apply a scale factor to its side of x, the area increases by a factor of x^2,and the volume increases by a factor of x^3.

Answer 22

ok

Answer 23

Here, the scale factor on the side is 3, so the scale factor on the volume is 3^3.
3^3 = 3 * 3 * 3 = 27
That means the new volume is 27 times larger than the original one.
90 cm^3 * 27 = 2430 cm^3