Question

Pyramid A is a dilation with scale factor 4 of pyramid B. What is the volume of pyramid A in terms of the volume of pyramid B?

a) 0.25 times Va
b) 2 times Va
c) 8 times Va
d) 64 times Va

Answer 1

The volume of a pyramid is given by the formula:

V = (1/3) * B * h

where B is the area of the base and h is the height of the pyramid.

If pyramid A is a dilation with scale factor 4 of pyramid B, then the ratio of their corresponding side lengths is 4:1. Since volume is a cubic function of length, the ratio of their volumes is the cube of the scale factor:

V_A / V_B = (4/1)^3 = 64

Therefore, the volume of pyramid A is 64 times the volume of pyramid B.

The answer is (d) 64 times Va.