A triangular prism has a volume of 10 cm3. If each dimension of the prism is multiplied by four, what is the new volume of the prism?

Question

A triangular prism has a volume of 10 cm3.  If each dimension of the prism is multiplied by four, what is the new volume of the prism?

rulnick · Answer

4^3 times 10 cm^3, or 640 cm^3.

mertsj · Answer

640

mertsj · Answer

You are introducing a factor of 4 to each dimension and then you multiply three dimensions together (base, height of triangle and height of prism).  So you multiply 4x4x4 which makes the volume 64 times greater.

mertsj · Answer

Do you understand?

directrix · Answer

If the scale factor of two similar solids is a:b, then the ratio of their volumes is a ³  :b ³ .

The prism formed by quadrupling each edge of the first prism is similar to the original one with scale factor 4:1. Cube that ratio to get  64.1 .Then, 10/ v = 1/64. Volume is 640 cubic cm.