Question

If a cone has the same radius and height as a cylinder, the volume of the cone is (one fourth, one third, half, or two thirds) the volume of the cylinder. If a cylinder and a sphere have the same radius and the cylinder’s height is twice its radius, then the volume of the sphere is (one fourth, one third, half, or two thirds) the volume of the cylinder.

Answer 1

Explanation:

radius of cone, rco

height of cone, hco

radius of cylinder, rcy

height of cylinder, hcy

radius of sphere, rs

volume of cone, vco = pi × rco^2 × hco/3

volume of cylinder, vcy = pi x rcy^2 × hcy

volume of sphere, vs = pi × (4/3)r^3

if rco = rcy = r and hco = hcy = h, then

vco = (pi × r^2 × h)/3

vcy = pi x r^2 ×h

=> vco = vcy/3

vco is one third vcy

if rcy = rs = r and hcy = 2rs = 2r, then

vcy = pi × r^2 × 2r = 2pi x r^3

vs = 4/3 (pi x r^3) = 2/3 (2pi × r^3)

=> vs = 2/3 vcy

vs is two thirds vcy