Chapter 12.2, Problem 17PPS

To determine

Find the lateral area and surface area given cereal container.

Answer to Problem 17PPS

L = $1484.8c{m}^2$

S = $1745.2c{m}^2$

Explanation of Solution

Given:

  

Formula Used:

The Lateral area L is

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

The Surface area S is

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

Calculation:

The base of the container is a rectangle , whose length is 18.6 cm and width is 7 cm.

Perimeter of the base = P =2(length + width ) = 2 (18.6 +7 ) = 51.2 cm.

Lateral area = Ph

Substitute P = 51.2 , h = 29 ;

So , Lateral area = L = $Ph=51.2(29)c{m}^2=1484.8c{m}^2$

Area of the base = B = $(length\text{ of rectangle)(width of rectangle)=}(18.6)(7)=130.2c{m}^2$

Surface area of container = L + 2B = 1484.8+2(130.2) = 1484.8+260.4 = $1745.2c{m}^2$

Hence ,

L = $1484.8c{m}^2$

S = $1745.2c{m}^2$