how to find volume 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 [latex]\pi [/latex] with [latex]3.14[/latex].

Volume and Surface Area of a Sphere

For a sphere with radius [latex]r\text{:}[/latex]

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 [latex]6[/latex] 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 [latex]V[/latex] = volume
Step 4. Translate. Write the appropriate formula.	[latex]V=\frac{4}{3}\pi {r}^{3}[/latex]
Step 5. Solve.	[latex]V\approx \frac{4}{3}\left(3.14\right){6}^{3}[/latex] [latex]V\approx 904.32\text{cubic inches}[/latex]
Step 6. Check: Double-check your math on a calculator.
Step 7. Answer the question.	The volume is approximately [latex]904.32[/latex] 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.	[latex]S=4\pi {r}^{2}[/latex]
Step 5. Solve.	[latex]S\approx 4\left(3.14\right){6}^{2}[/latex] [latex]S\approx 452.16[/latex]
Step 6. Check: Double-check your math on a calculator
Step 7. Answer the question.	The surface area is approximately [latex]452.16[/latex] square inches.

try it

example

A globe of Earth is in the shape of a sphere with radius [latex]14[/latex] centimeters. Find its 1. volume and 2. surface area. Round the answer to the nearest hundredth.