Things You'll Need:
- Calculator
-
Step 1
Solve surface area problem of any geometric figure when given its volume by knowing the formulas. For instance, the formula for surface area of a sphere is given by SA= 4π(r^2), while its volume (V) is equal to (4/3)π(r^3) where "r" is the radius of the sphere. Note that most formulas for surface area and volume for various figures are available online (see the Resources).
-
Step 2
Use the formulas in Step 1 to calculate the surface area for a sphere with a volume of 4.5π cubic feet where π (pi) is approximately 3.14.
-
Step 3
Find the radius of the sphere by substituting 4.5π ft^3 for V in the formula in Step 1 to get:
V=4.5π cubic feet.= (4/3)π(r^3) -
Step 4
Multiply each side of the equation by 3 and the equation becomes:
13.5 π cubic feet =4π(r^3) -
Step 5
Divide both sides of the equation by 4π in Step 4 to solve for the radius of the sphere. To get:
(13.5π cubic feet)/(4π) =(4π )(r^3)/ (4π), which then becomes:
3.38 cubic feet= (r^3) -
Step 6
Use the calculator to find the cubic root of 3.38 and subsequently the value of the radius "r" in feet. Find the function key designated for cubic roots, press this key and then enter the value 3.38. You find that the radius is 1.50 ft. You can also use an online calculator for this calculation (see the Resources).
-
Step 7
Substitute 1.50 ft. in the formula for SA= 4π(r^2) found in Step 1. To find:
SA = 4π(1.50^2) = 4π(1.50X1.50) is equal to 9π square ft.
Substituting the value for pi= π= 3.14 in the answer 9π square ft., you find that the surface area is 28.26 square ft. To solve these types of problems, you need to know the formulas for both surface area and volume.
