Chapter 12.3, Problem 35WE

To determine

To calculate: The volume and draw the diagram

Answer to Problem 35WE

The volume of the cone is 25.45 $c{m}^3$

  

Explanation of Solution

Given information: Consider the given information,

A cone is inscribed in a regular square pyramid

Slant height = 9 cm

And base edge = 6 cm

  $\pi \approx 3.14$

Formula used: Consider the given formula,

r = radius, h = height

Volume = $\frac{1}{3}\pi r^{2}h$

Calculation : Consider the given information the formula is,

  $2r=6$

  $r=3cm$

  $h=\sqrt{{(9)}^2-{(3)}^2}$

  $h=6\sqrt{2}cm$

The volume of cone = $\frac{1}{3}\pi \times {(3)}^2\times 6\sqrt{2}=25.45c{m}^3$