Question

The volume V of a pyramid varies jointly as the area of it’s base B and its height h. If the volume of the pyramid is 24 cubic meters when the area of it’s base is 18 square meters and its height is 4 meters find the volume of a pyramid when the area of it’s base is 21 square meters and its height is 7 meters.

Answer 1

v = k B h
24 = k* 18 * 4
k = 24 / 72 = 1/3 If you did not already know volume of pointy object with straight sides = (1/3) * base area * height
so
V = (1/3) * 21 * 7 = 7 * 7 = 49

Answer 2

Volume = k(base)(height)
given: Vol = 24 m^3, base = 18 m^2 , height = 4 m
24 m^3 = k(18)(4) m^3
k = 24/(18*4) = 1/3
Vol = (1/3)(base)(height)
when base = 21, height = 7
Vol = (1/3)(21 m^2)(7 m) = 49 m^3

Answer 3

What a good answer. Brilliant girl.