Question

The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same.

The volume of pyramid A is ____ the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is ______the volume of pyramid A.

Answer 1

The volume of pyramid A is twice the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is equal to the volume of pyramid A.

Explanation:

edmentum answer

Answer 2

The volume of a pyramid is expressed as the product of its length, width and height divided by three. We first solve the volume of pyramids A and B.

Volume of A = (10 x 20 x h) / 3 = 200h / 3
Volume of B = (10 x 10 x h) / 3 = 100h/3

Since the heights of the two pyramid are the same we can substitute on equation to the other in terms of h.

Volume of A = (200 x 3 x Volume of B) / (100 x 3)
Volume of A = 2 x Volume B
Thus, the volume of A is twice the volume of B.

If the height of pyramid B is twice of pyramid A, the new volume of pyramid B is equal to the volume of pyramid A.