How to Find the Surface Area of Basic 3-D Figures

Add some depth to your area of the world.

Difficulty:

Moderately Easy

Instructions

Things You'll Need

• Drawing Books
• Calculators
• Drafting Compasses
• Erasers
• Folders
• Graph Papers
• Notebooks
• Rulers

Cubes, Prisms and Spheres

1. Find the surface area of a cube by squaring the length of one side and multiplying the result by 6. Example: The surface area of a cube with side length 3 is 6 x (3 x 3) = 54.

2. Calculate the area of each side and find the sum of the areas of all sides to find the surface area of a prism. Example: the surface area of a rectangular prism of height 2, width 3, and length 5 is (2 x 3) + (2 x 3) + (2 x 5) + (2 x 5) + (3 x 5) + (3 x 5) = 62.

3. Multiply the square of the radius by pi to find the surface area of a sphere. Then multiply the result by 4. Example: The surface area of a sphere of radius 3 is 4 x pi x 3 x 3 = 113.

Cylinders and Cones

1. Find the surface area of a cylinder by first multiplying the radius by 2 times pi.

2. Multiply the product by the height of the cylinder.

3. Multiply the square of the radius by 2 times pi.

4. Find the sum of the results of steps 5 and 6. Example: The surface area of a cylinder of radius 4 and height 5 is (2 x pi x 4 x 5) + (2 x pi x 4 x 4) = 226.

5. Determine the surface area of a cone by multiplying the radius of the base by the slant height of the cone.

6. Multiply the result by pi.

7. Multiply the square of the radius of the base by pi.

8. Find the sum of the results of steps 9 and 10. Example: The surface area of a cone with base radius 2 and slant height 4 is (pi x 2 x 4) + (pi x 2 x 2) = 38.