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Study Guides > Prealgebra

Finding the Volume and Surface Area of a Sphere

Learning Outcomes

  • Find the volume and surface area of a sphere
 

A sphere is the shape of a basketball, like a three-dimensional circle. Just like a circle, the size of a sphere is determined by its radius, which is the distance from the center of the sphere to any point on its surface. The formulas for the volume and surface area of a sphere are given below. Showing where these formulas come from, like we did for a rectangular solid, is beyond the scope of this course. We will approximate π\pi with 3.143.14.

Volume and Surface Area of a Sphere

For a sphere with radius r:r\text{:} An image of a sphere is shown. The radius is labeled r. Beside this is Volume: V equals four-thirds times pi times r cubed. Below that is Surface Area: S equals 4 times pi times r squared.
 

example

A sphere has a radius 66 inches. Find its 1. volume and 2. surface area. Solution Step 1 is the same for both 1. and 2., so we will show it just once.
Step 1. Read the problem. Draw the figure and label it with the given information. .
1.
Step 2. Identify what you are looking for. the volume of the sphere
Step 3. Name. Choose a variable to represent it. let VV = volume
Step 4. Translate. Write the appropriate formula. V=43πr3V=\frac{4}{3}\pi {r}^{3}
Step 5. Solve. V43(3.14)63V\approx \frac{4}{3}\left(3.14\right){6}^{3} V904.32cubic inchesV\approx 904.32\text{cubic inches}
Step 6. Check: Double-check your math on a calculator.
Step 7. Answer the question. The volume is approximately 904.32904.32 cubic inches.
2.
Step 2. Identify what you are looking for. the surface area of the cube
Step 3. Name. Choose a variable to represent it. let S = surface area
Step 4. Translate. Write the appropriate formula. S=4πr2S=4\pi {r}^{2}
Step 5. Solve. S4(3.14)62S\approx 4\left(3.14\right){6}^{2} S452.16S\approx 452.16
Step 6. Check: Double-check your math on a calculator
Step 7. Answer the question. The surface area is approximately 452.16452.16 square inches.
 

try it

[ohm_question]146804[/ohm_question]
   

example

A globe of Earth is in the shape of a sphere with radius 1414 centimeters. Find its 1. volume and 2. surface area. Round the answer to the nearest hundredth.

Answer: Solution

Step 1. Read the problem. Draw a figure with the given information and label it. .
1.
Step 2. Identify what you are looking for. the volume of the sphere
Step 3. Name. Choose a variable to represent it. let VV = volume
Step 4. Translate. Write the appropriate formula. Substitute. (Use 3.14 for π\pi ) V=43πr3V=\frac{4}{3}\pi {r}^{3} V43(3.14)143V\approx \frac{4}{3}\left(3.14\right){14}^{3}
Step 5. Solve. V11,488.21V\approx 11,488.21
Step 6. Check: We leave it to you to check your calculations.
Step 7. Answer the question. The volume is approximately 11,488.2111,488.21 cubic inches.
2.
Step 2. Identify what you are looking for. the surface area of the sphere
Step 3. Name. Choose a variable to represent it. let S = surface area
Step 4. Translate. Write the appropriate formula. Substitute. (Use 3.14 for π\pi ) S=4πr2S=4\pi {r}^{2} S4(3.14)142S\approx 4\left(3.14\right){14}^{2}
Step 5. Solve. S2461.76S\approx 2461.76
Step 6. Check: We leave it to you to check your calculations.
Step 7. Answer the question. The surface area is approximately 2461.762461.76 square inches.

 

try it

[ohm_question]146806[/ohm_question]
 

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