Finding 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.

volume and surface area of a sphere

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

 

 

Note: We will approximate [latex]\pi[/latex] with [latex]3.14[/latex].

A sphere has a radius [latex]6[/latex] inches. Find its:

1. volume
2. surface area

Show 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=\Large\frac{4}{3}\normalsize\pi {r}^{3}[/latex]
   Step 5. Solve.	[latex]V\approx \Large\frac{4}{3}\normalsize\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.