Question

A sphere with a radius of 6 cm has the same volume as a cone with a height of 6 cm. What is the radius of the cone?

A) 2 cm

B) 4 cm

C) 8 cm

D) 12 cm

Answer 1

Answer:

D) 12 cm

Step-by-step explanation:

The volume of a sphere is

V_s = 4/3 * pi * r_s^3

The volume of a cone is

V_c = 1/3 * pi * h * r_c^2

Since we know that the two volumes are equal, we can say

V_s = V_c

4/3 * pi * r_s^3 = 1/3 * pi * h * r_c^2

Let us now isolate r_c, the radius of the cone:

4/3*r_s^3 = 1/3 *h*r_c^2

sqrt((4*r_s^3)/h) =r_c = 12 cm  

So the radius of the cone is 12 cm

Answer 2

Answer:

Option D

Volume of cone = 1/3 π r² h

Volume of sphere = 4/3 π r³

4/3 π(6)³ = 1/3 π r²(6)

== 4(6)³ = r²(6)

== (2²)(6)² = r²

== r = 12 cm