Question

The relationships of the volumes of cylinders, cones, and spheres (considering that the height and radius are the same for all of the objects) are stated below.

Fill in the blank with the correct number.

(5 points)
A. One sphere +
3
cone(s) = one cylinder

B.
cone(s) = one cylinder

C.
cone(s) = one sphere

D. One sphere =
cylinder

E. One cone =
cylinder

Answer 1

Use h = 2r (sphere diameter = cylinder/cone height). Volumes: V_cyl = πr^2h = 2πr^3, V_cone = (1/3)πr^2h = 2/3πr^3, V_sphere = 4/3πr^3 = 4/3πr^3.

Thus:
A. 1
B. 3
C. 2
D. 2/3
E. 1/3