Chapter 12.4, Problem 26WE

To determine

To show: The area of sphere is equals the lateral area of the cylinder.

Answer to Problem 26WE

The area of the sphere is equals the lateral area of the cylinder.

Explanation of Solution

Given information:

A sphere is inscribed in a cylinder.

Calculation:

Since, the sphere with radius r is inscribed in the cylinder. Therefore,

Radius of the cylinder will be same as sphere that is r and height will be 2r.

The area of cylinder is given by

  $A=2\pi rh$ where $r$ is the radius of the cylinder and $h$ is the height.

And, area of sphere is given by,

  $A=4\pi r^2$........(1)

where r is the radius of the sphere.

Since, radius of the cylinder is $r$ and height is $h=2r$ .

Therefore, area of the cylinder is

  $\begin{array}{l}A=2\pi rh\\ A=2\pi r\left(2r\right)\\ A=4\pi r^2\end{array}$........(1)

Thus, from equation (1) and (2) the area of the sphere is equals the lateral area of the cylinder.

Hence,

The area of the sphere is equals the lateral area of the cylinder.