Box A has a volume of 32 cubic meters. Box B is similar to box A. To create box B, box A's dimensions were tripled. What is the volume of box B?

a. 864 m3
b. 288 m3
c. 96 m3
d. 32 m3

Question

Box A has a volume of 32 cubic meters. Box B is similar to box A. To create box B, box A's dimensions were tripled. What is the volume of box B? 

a. 864 m3
b. 288 m3
c. 96 m3
d. 32 m3

anonymous · Answer

If you triple the dimensions you have to multiply by a factor of 27 for cubes. You can find this through experimentation with existing values, such as 1x1x1 becoming 3x3x3.

anonymous · Answer

The alternative would be taking the cubed root of 32, multiplying that by 3, and then cubing it.

anonymous · Answer

The cubed root would be used to find 1 side as the volume of a cube is sidexsidexside or side cubed.

anonymous · Answer

And in regards to my first method, be cautious as you typically cannot generalize rules like this in higher level mathematics.

directrix · Answer

Theorem:
If two solids are similar, the cube of the scale factor of the two solids is equal to the ratio of the volumes.

The two boxes are similar and have a scale factor of 1/3 from small to large.

(1/3)^3 = 32/ V where V is the Volume of the larger box.

1/27 = 32/V

V = ?     @lowcard2

anonymous · Answer

v=96 then?

directrix · Answer

Yes, 96 cubic meters.

anonymous · Answer

I disagree, is it not 864? The factor discussed was 1:27. 32:864 would fit that factor.