Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder have the same height and radius. The volume of the cylinder is 27pi ft. What equation gives the volume of the sphere ?

Answer 1

Explanation:

radius of sphere, rs

radius of cylinder, rc

height of cylinder, h

given: h = rs = rc =r..eq1

volume of cylinder, vc = 27pi ft...eq2

volume of cylinder, vc = pi × rc^2 × h...eq3

volume of sphere, vs = 4/3(pi×rs^3)...eq4

subst for h & rs from eqn 1 in eqn 3...

vc = pi x r^2 x r= pi x r^3...eqn 5

subst for vc from eqn 2 in eqn 5...

=> 27 pi ft = pi x r^3

=> 27 = r^3

=> r = 3ft...eqn 6

subst for rs from eqn 1 in eqn 4

vs = 4/3 (pi x r^3)...eqn7

subst for pi x r^3 from eqn 5 in eqn 7

vs = 4/3 vc = 4/3 (27pi ft) = 36 pi ft

Answer 2

The equation of the volume of the sphere is 4/3 × 27π

The volume of a cylinder is expressed as

V = πr²h

Since the cylinder has thesame height and radius, therefore, the volume of the cylinder will now be

V = πr² × r

V = πr³

The volume of a sphere is expressed as

V = 4/3(πr³)

Therefore we can say

the volume of sphere = 4/3 × volume of the cylinder

Volume of cylinder = 27π

volume of sphere = 4/3 × 27π

= 4 × 9

= 36πft³