A triangular pyramid has a volume of 25 ft³. If all its dimensions are doubled, the volume of the new pyramid will be _____ ft³.

Question

mathstudent55 · Answer

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mathstudent55 · Answer

Here are two cubes.
One has measures 3 by 3 by 3.
The other one has measures 6 by 6 by 6.
As you can see the second one has all sides double of the the first one.

mathstudent55 · Answer

Can you calculate the volumes of the two cubes?

anonymous · Answer

27 and 216

mathstudent55 · Answer

Exactly.

V1 = 3 x 3 x 3 = 27

V2 = 6 x 6 x 6 = 216

mathstudent55 · Answer

Now divide the volume of the second cube by the volume of the first one.

What is 216/27 ?

anonymous · Answer

8

mathstudent55 · Answer

Good.
The sides went up by 2 times, and the volume went up by 8 times.
Notice 8 = 2^3.

This is the general rule:

If two similar figures have a scale factor of s, the scale factor of the areas is s^2 and the scale factor of the volumes is s^3.

Since in your case the scale factor of the sides is 2, the scale factor of the volumes is 2^3 = 8.
The new volume is 8 times the original volume.

anonymous · Answer

Awesome! Thanks!(:

mathstudent55 · Answer

wlcm