SOLVING SURFACE AREA PROBLEMS

We may need to find surface area of different figures to solve many real-world problems. 

In this section, we are going to see, how surface area of figures can be used to solve real world problems. 

Let us see, how to find surface area of a prism. 

Examples

Example 1 : 

Erin is making a jewelry box of wood in the shape of a rectangular prism. The jewelry box will have the dimensions shown below. The cost of painting the exterior of the box is $0.50 per square in. How much does Erin have to spend to paint the jewelry box ?

Solution : 

To know that total cost of painting, first we have to know the Surface area of the jewelry box. 

Find surface area of the box. 

Step 1 :

Identify a base, and find its area and perimeter.

Any pair of opposite faces can be the bases. For example, we can choose the bottom and top of the box as the bases.

Find base area. 

B  =  l x w

B  =  12 x 15

B  =  180 square in.

Find perimeter of the base. 

P  =  2(12) + 2(15)

P  =  24 + 30

P  =  54 in.

Step 2 : 

Identify the height, and find the surface area.

The height h of the prism is 6 inches. Use the formula to find the surface area.

S  =  Ph + 2B

S  =  54(6) + 2(180)

S  =  684 square inches

Step 3 :

Total cost  =  Area x Cost per square in.

Total cost  =  684 x $0.50

Total cost  =  $342

So, Erin has to spend $342 to paint the jewelry box. 

Example 2 : 

A metal box that is in the shape of rectangular prism has the following dimensions. The length is 9 inches, width is 2 inches, and height is 1 1/2 inches. Find the total cost of silver coating for the entire box. 

Solution : 

To know that total cost of silver coating, first we have to know the Surface area of the metal box. 

Find surface area of the box. 

Step 1 :

Identify a base, and find its area and perimeter.

Any pair of opposite faces can be the bases. For example, we can choose the bottom and top of the box as the bases.

Find base area. 

B  =  l x w

B  =  9 x 2

B  =  18 square in.

Find perimeter of the base. 

P  =  2(9) + 2(2)

P  =  18 + 4

P  =  22 in.

Step 2 : 

Identify the height, and find the surface area.

The height h of the prism is 1 1/2 inches. Use the formula to find the surface area.

S  =  Ph + 2B

S  =  22(1 1/2) + 2(18)

S  =  22(3/2) + 36

S  =  33 + 36

S  =  69 square inches

Step 3 :

Total cost  =  Area x Cost per square in.

Total cost  =  69 x $1.50

Total cost  =  $103.50

So, the total cost of silver coating for the entire box is $103.50. 

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