# How to Calculate Surface Area From Volume

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In geometry, students must often calculate surface areas and volumes of different geometric shapes such as spheres, cylinders, rectangular prisms or cones. For these types of problems, it is important to know the formulas for both surface area and volume of these figures. It also helps to understand what the definitions of surface area and volume are. Surface area is the total area of all exposed surfaces of a given three-dimensional figure or object. Volume is the amount of space occupied by this figure. You can easily calculate surface area from volume by applying the right formulas.

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= 4?(r^2), while its volume (V) is equal to (4/3)?(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).

Use the formulas in Step 1 to calculate the surface area for a sphere with a volume of 4.5? cubic feet where ? (pi) is approximately 3.14.

Find the radius of the sphere by substituting 4.5? ft^3 for V in the formula in Step 1 to get: V=4.5? cubic feet.= (4/3)?(r^3)

Multiply each side of the equation by 3 and the equation becomes: 13.5 ? cubic feet =4?(r^3)

Divide both sides of the equation by 4? in Step 4 to solve for the radius of the sphere. To get: (13.5? cubic feet)/(4?) =(4? )(r^3)/ (4?), which then becomes: 3.38 cubic feet= (r^3)

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).

Substitute 1.50 ft. in the formula for SA= 4?(r^2) found in Step 1. To find: SA = 4?(1.50^2) = 4?(1.50X1.50) is equal to 9? square ft.

Substituting the value for pi= ?= 3.14 in the answer 9? 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.

#### Tips

• A T1-83 Plus calculator was used to find the cubic root in Step 6. Using this calculator to find a solution, you must press the “MATH” function key first and then find the function key for cubic roots. Since there may be differences in the use of other calculator models, check the user manuals for instructions on calculating cubic roots.