Chapter 12.2, Problem 18PPS

To determine

Find the lateral area and surface area given cereal container.

Answer to Problem 18PPS

L = $1000.6c{m}^2$

S = $1266c{m}^2$

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 circle , whose diameter is 13 cm .

Perimeter of the base of the container = P = $2\pi r=2\pi \left(\frac{13}{2}\right)=40.84cm$

Lateral area = Ph

Substitute P = 40.84 , h = 24.5 ;

So , Lateral area = L = $Ph=40.84(24.5)c{m}^2\approx 1000.6c{m}^2$

Area of the base = B = $\pi r^2=\pi {\left(\frac{13}{2}\right)}^2=132.7c{m}^2$

Surface area of prism = L + 2B = 1000.6+2(132.7) = 1000.6 + 265.4 = $1266c{m}^2$

Hence ,

L = $1000.6c{m}^2$

S = $1266c{m}^2$