A sphere and a right circular cylinder both have radius r. The height of the cylinder is 18. For what value of r will the volume of the sphere be twice the volume of the cylinder?

Answer 1

V_s = (4/3)πr³

V_c.= πr²h

V_s= 2V_c

(4/3)πr³ = 2πr²18 π's cancel out and can divide both sides by r².

(4/3)r = 2(18) Multiply both sides by 3/4.

r = 2(18)(3/4)

r = 27

Check: V_s = 82448; V_c = 41224

Answer 2

(4/3)πr³ = 18πr²

r = 18 / (4/3)