Chapter 12.4, Problem 55SPR

To determine

Find the area of the inside of the pan that needs to be coated.

Answer to Problem 55SPR

Area of the inside of the pan that needs to be coated is $205i{n}^2$ .

Explanation of Solution

Given:

A rectangular cake pan is 9 inches by 13 inches by 2 inches deep.

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.

Calculation:

The base of the pan is rectangle , whose length is 13 in. and width is 9 in.

Perimeter of the base of the rectangle= P = 2(13) + 2(9) = 26+18 = 44 in. [perimeter of rectangle = 2(length) + 2(width) ]

Lateral area = Ph

Substitute P = 44 , h = 2 ;

So , Lateral area = L = $Ph=44\cdot 2i{n}^2=88i{n}^2$

The base is reactangle , whose length is 13 in. and width is 9 in.

Area of the base of the pan = B = $13\cdot 9=117i{n}^2$ [area of rectangle = (length)(width) ]

Area of the inside of the pan that needs to be coated. = L + B = 88 + 117 = $205i{n}^2$

Hence ,

Area of the inside of the pan that needs to be coated is $205i{n}^2$ .