Chapter 12, Problem 1PST

To determine

To calculate : The radius of the cone.

Answer to Problem 1PST

The radius of the cone would be $9mm$

Explanation of Solution

Given information : A right circular cone has a height that is twice its base radius, and the lateral surface area is given as $569m{m}^2$ .

Formula used : The lateral surface area of the cone is $\pi rl$ . And the slant height is $l=\sqrt{r^2+h^2}$ . Where $r$ is the radius and $l$ is the slant height of the cone and $h$ is the height of the cone.

Calculation : Calculate the slant height in terms of radius.

  $l=\sqrt{r^2+h^2}$

  $\begin{array}{l}l=\sqrt{r^2+{(2r)}^2}\\ l=\sqrt{r^2+4r^2}\\ l=\sqrt{5r^2}\\ l=r\sqrt{5}\end{array}$

Now, using the given lateral surface area.

  $\pi rl=569$

Plug the slant height, find the radius.

  $\begin{array}{l}\pi r\times r\sqrt{5}=569\\ \sqrt{5}\pi r^2=569\\ r=\sqrt{\frac{569}{\sqrt{5}\pi }}\\ r=9mm\end{array}$