Surface Area
- Cube: 6 l² (l=length of a side of the cube)
- Prism: Ph+2B (B=area of base of shape; p=perimeter of base; h=height)
- Sphere: 4πr² (use 3.14 for π; r=radius)
- Cylinder: 2πr²+2πrh (r=radius; h=height of cylinder)
- Pyramid: B+1/2 Pl (P=perimeter, l=slant height, B=area of base of pyramid)
- Cone: πr²+πrl (r=radius, l=slant height)
Surface Area Example
If a cone has a slant height of 17 cm and a radius of 9 cm. What would the surface area be?
πr²+πrl=s → write out the formula
3.14×9²+3.14×9×17=s → substitute with given numbers
254.34+480.42=s → solve on both sides
734.76=s → add together
s=734.76 → put the variable before the number
πr²+πrl=s → write out the formula
3.14×9²+3.14×9×17=s → substitute with given numbers
254.34+480.42=s → solve on both sides
734.76=s → add together
s=734.76 → put the variable before the number
Pyramid and Sphere Surface Area Practice Problem
1. A pyramid with a base of 4 inches and a height of 5 inches on the bottom. The slant height is 3 times the height of the height on the base. What is the surface area?
2. The radius on a sphere is 27 cm. What is the surface area?
Answer Key
2. The radius on a sphere is 27 cm. What is the surface area?
Answer Key