Chapter 12.2, Problem 32PPS

(a)

To determine

Find the lateral area of the shade.

Answer to Problem 32PPS

  $381.7i{n}^2$

Explanation of Solution

Given:

The lamp shade is a cylinder of height 18 inches with a diameter of $6\frac{3}{4}$ inches.

Formula Used:

The Lateral area L of a cylinder with radius r and height h :

  $L=2\pi rh$

Calculation:

diameter = $6\frac{3}{4}=\frac{27}{4}=6.75$ inches

radius = r = $\frac{6.75}{2}=3.375$ inches

h = 18 inches

Lateral area of the shade = $L=2\pi rh=2\pi (3.375)(18)=381.7i{n}^2$

(b)

To determine

Find the lateral area if the height is divided by 2.

Answer to Problem 32PPS

Lateral area becomes half.

Explanation of Solution

Calculation:

From part (a) , Lateral area = $L=381.7i{n}^2$

Now, height becomes half of previous height

  $h_1=\frac{h}{2}$ , radius is same, $r_1=r$ as part (a) ,

Lateral surface area now = $L_1=2\pi r_1{h}_1=2\pi r\frac{h}{2}=\frac{1}{2}(2\pi rh)=\frac{1}{2}L$

So, the lateral area becomes half of the original lateral area , if the original height is divided by 2 .