The prism has a volume of 120 cm3. What would the volume of the prism be if each dimension were halved? cm3 Triangular prism with unlabeled dimensions

The volume of a triangular prism is V = 1/2 x a x c x h where a is height of the triangle, c is the base of the triangle and h is the height of the prism.

120 = 1/2 x a x c x h; we write a from the previous equation in terms of c and h thus,

a = 240 / (c x h)

If the dimensions where halved then a = a/2; c = c/2; h=h/2

We use the volume formula again and substitute the given values to find the new volume,

V = 1/2 x a/2 x c/2 x h/2

Substitute the previously determined a term,

V = 1/2 x (240/2ch) x c/2 x h/2

We cancel and evaluate the constants therefore the new volume is,

V = 15 cm^3