Surface Area and Volume: Surface Area and Volume of Spheres

Surface area and Volume of a Sphere: Examples

Example 1:
Find the surface area and volume of a sphere with radius 6 ft.

Sphere with radius 6 feet
Sphere

 

Solution:
SA = 4πr² =  4π(6)² = 144π ft²
V = four-thirds pi r-cubed = four-thirds pi times 6 cubed equals 288 pi ft³

Example 2:
Find the surface area and volume of a sphere with diameter 25 in.

Sphere with diameter 25 in
Sphere

 

Solution:
Both formulas use the length of the radius, so the first step is to find the length of the radius.

r = one-half d equals one-half times 25 equals 12 point 5 

SA = 4πr² =  4π(12.5)² = 625π in²

V = four-thirds pi r-cubed = four-thirds pi times 12 point 5 cubed equals the quotient 15 thousand 625 pi divided by 6 in³