The surface area of a three-dimensional figure is the sum of the areas of all its faces.

Example of Surface Area

The formula for the total surface area of a cone is πr^{2} + πrl.
= π × 10^{2} + π × 10 × 39
= 100π + 390π
= 490π

Video Examples: Surface Area

Solved Example on Surface Area

Ques: An oil tank is 42 ft tall with a diameter of 88 ft. What is its surface area? Take π = 3.

Choices:

A. 22,704 square feet
B. 22,703 square feet
C. 23,763 square feet
D. 22,705 square feet
Correct Answer: A

Solution:

Step 1: The oil tank is in the shape of a cylinder.
Step 2: The cylinder has two circles and one rectangle.
Step 3: So, the surface area of the oil tank = 2 × area of the circle + area of the rectangle.
Step 4: Surface area = 2πr^{2} + bh
Step 5: = 2 × 3 × 44 × 44 + 2 × 3 × 44 × 42
Step 6: = 11,616 + 11,088 = 22,704 square feet
Step 7: The surface area of the oil tank = 22,704 square feet.