Question

Which of the following solid figures have a volume of 36π cubic units? Select all that apply.

a cone with a diameter of twelve units and a height of three units
a sphere with a radius of three units
a cone with a radius of three units and a height of four units
a cylinder with a diameter of six units and a height of one unit

Answer 1

Compute each volume.

1) Cone, diameter 12 → r = 6, h = 3:
V = (1/3)πr^2h = (1/3)π(6^2)(3) = (1/3)π(36)(3) = 36π → matches.

2) Sphere, r = 3:
V = (4/3)πr^3 = (4/3)π(27) = 36π → matches.

3) Cone, r = 3, h = 4:
V = (1/3)π(3^2)(4) = (1/3)π(9)(4) = 12π → not 36π.

4) Cylinder, diameter 6 → r = 3, h = 1:
V = πr^2h = π(3^2)(1) = 9π → not 36π.

So the figures with volume 36π are the first cone and the sphere (options 1 and 2).