Chapter 12.3, Problem 36WE

To determine

To find: The ratio of the radius and the slant height

Answer to Problem 36WE

The ratio of the radius and slant height is 3:2

Explanation of Solution

Given information: Consider the given information,

The lateral area of a cone is three-fifths the total area

Formula used: Consider the given formula,

r = radius, h = height

Slant height = $\sqrt{h^2+r^2}$

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

Calculation : Consider the given information the formula is,

  $\pi r\sqrt{h^2+r^2}=\frac{3}{5}\pi r^2+\pi r\sqrt{h^2+r^2}$

  $r\sqrt{h^2+r^2}=\frac{3}{5}{r}^2+r\sqrt{h^2+r^2}$

  $5r\sqrt{h^2+r^2}=3r^2+r\sqrt{h^2+r^2}$

  $2r\sqrt{h^2+r^2}=3r^2$

  $\sqrt{h^2+r^2}=\frac{3}{2}r$

  $\frac{\sqrt{h^2+r^2}}{r}=\frac{3}{2}=3:2$