Box A has a volume of 12 cubic meters. Box B is similar to box A. To create box B, box A's dimensions were multiplied by five. What is the volume of box B?

60 m3

300 m3

1,500 m3

7,500 m3

Question

Box A has a volume of 12 cubic meters. Box B is similar to box A. To create box B, box A's dimensions were multiplied by five. What is the volume of box B?

 60 m3

 300 m3

 1,500 m3

 7,500 m3

directrix · Answer

The theorem we need to use is the following:

If two solids are similar, the cube of the scale factor of the two solids is equal to the ratio of the volumes.

Box A ~ Box B with a 1:5 scale factor.

This is because Box B's dimensions are five times those of Box A.

directrix · Answer

The equation is this:

(scale factor)^3 = Box A Volume/Box B Volume

(1/5)³  = 12/B where B is the volume of Box B.

@luka1998 

Solve this for B:  (1/5)³  = 12/B

anonymous · Answer

0.008 
B=0.096

directrix · Answer

Sorry for the delay. The messaging system here is not working.

directrix · Answer

I did not get what you did.

(1/5)³ = 12/B

1/125 = 12/B

Cross Multiply

B = 12 * 125

B = ? @luka1998

anonymous · Answer

1,500

directrix · Answer

1500 cubic meters is what I got for the volume of Box B.

anonymous · Answer

@Directrix  thx