We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# Nice question, help!

0
411
2

A right circular cone is inscribed in a right prism as shown. What is the ratio of the volume of the cone to the volume of the prism? Express your answer as a common fraction in terms of $$\pi$$ . Mar 21, 2018

### 2+0 Answers

#1
0

A right circular cone is inscribed in a right prism as shown. What is the ratio of the volume of the cone to the volume of the prism? Express your answer as a common fraction in terms of  pi.   Mar 21, 2018
edited by Omi67  Mar 21, 2018
#2
+1

Let the height of the prism = H

Since the cone touches all four sides of the prism, the base must be square

So.....Let S be the side of the prism

So.....the volume of the prism is  S^2 *H  (1)

The radius of the cone  =  (1/2)S  and its height is H

So....its  volume  is   (1/3)*pi *(1/2 S)^2 * H   = (1/12)*pi*S^2*H  (2)

So.....the  ratio of (2)  to (1)  is

(1/12)* pi * S^2 * H                    pi

________________  =            ___

S^2  * H                                12   Mar 21, 2018