Chapter 12.2, Problem 29PPS

(a)

To determine

Explain how to find the surface area of the portion that represents people who prefer to watch movies at home.

Answer to Problem 29PPS

  $82.56i{n}^2$

Explanation of Solution

Given:

The graphic shows the results of a survey in which people were asked where they like to watch movies . Suppose the film can is a cylinder 12 inches in diameter .

  

Calculation:

The diameter of the cylinder is 12 inches .

So, the radius = $\frac{12}{2}=6$ inches.

Area of the surface = A = $\pi r^2=\pi 6^2=36\pi$

The surface area of the portion that represents people who prefer to watch movies at home = 73% of area of the surface

= $0.73(36\pi )=82.56i{n}^2$

(b)

To determine

Find the surface area of the portion in part (a) , if the height of the film can is 3 inches.

Answer to Problem 29PPS

  $283.68i{n}^2$

Explanation of Solution

Given :

  

Formula Used:

The Lateral area L of a right prism is

L = Ph , where h is the height of the prism and P is the perimeter of a base.

The Surface area S of a right prism is

S = L + 2B , where L is its Lateral area and B is the area of a base.

Calculation:

From part (a) , The surface area of the portion that represents people who prefer to watch movies at home = B = $82.56i{n}^2$

The radius r of can = 6 inches.

The perimeter of the can = $2\pi r=2\pi (6)=12\pi$

So, the arc that represents the 73% of the surface area = $73\%(12\pi )=27.52$

The perimeter P that represents the 73% of the surface area = 27.52 + 2r = 27.52 +12= 39.52inches.

The Lateral surface area = L = Ph = $=39.52\times 3=118.56i{n}^2$

The Surface area of the portion that represents people who prefer to watch movies at home = L + 2B = $=118.56+2\times 82.56=283.68i{n}^2$