Volume of a Sphere Calculator

Volume of a Sphere Example 1

Find the volume of the sphere below to 1 decimal place.

We can use Calculator 1 to solve this problem.

The formula for the volume of a sphere is: \[ V = {4 \over 3} \pi r^3 \]

If we substitute the values of the radius into this equation, we get: \[ V = {4 \over 3} \pi (8)^3 = {4 \over 3} \pi (512) = {2048 \over 3} \pi \]

This gives us a final answer of: \[ V = 2144.7 \;\ cm^3 \;\ to \;\ 1 \;\ decimal \;\ place \]

Volume of a Sphere Example 2

A large inflatable ball has a radius of 1 ½ meters. What is the volume of the ball? Give your answer to 2 decimal places.

We can use Calculator 1 to solve this problem.

The formula for the volume of a sphere is: \[ V = {4 \over 3} \pi r^3 \]

If we substitute the values of the radius into this equation, we get: \[ V = {4 \over 3} \pi (1 {1 \over 2})^3 = {4 \over 3} \pi ({27 \over 8}) = {9 \over 2} \pi \]

This gives us a final answer of: \[ V = 14.14 \;\ m^3 \; to \;\ 2 \;\ decimal \;\ places \]

Volume of a Sphere Example 3

A basketball has a diameter of 9.55 inches. What is the surface area of the ball? Give your answer to 1 decimal place.

We can use Calculator 1 to solve this problem, but we need to change the measurement from Radius to Diameter.

The first step is to find the radius of the ball.

The diameter of the ball is 9.55 inches. To find the radius, we have to halve the diameter (or divide the diameter by 2).

\[ 9.55 \div 2 = 4.775 \; inches \]

The formula for the volume of a sphere is: \[ V = {4 \over 3} \pi r^3 \]

If we substitute the values of the radius into this equation, we get: \[ V = {4 \over 3} \pi (4.775)^3 = {4 \over 3} \pi (108.87298...) = 145.16398... \pi \]

This gives us a final answer of: \[ V = 456.0 \;\ in^3 \; to \; 1 \; decimal \; place \]

Volume of a Sphere Example 4

A ball has a surface area of 500 square cm. What is the diameter of the ball? Give your answer to 1 decimal place.

In this case, we know the volume of the ball, but we need to find the diameter.

We can use Calculator 2 to solve this problem.

The formula for the volume of a sphere is: \[ V = {4 \over 3} \pi r^3 \]

This means that: \[ r^3 = V \div ({4 \over 3} \pi) = V \times {3 \over 4 \pi } = { 3V \over 4 \pi } \]

This means that the radius \[ r = \sqrt [\raise{7pt} \Large 3] ({ 3V \over 4 \pi}) \]

If we substitute the values of the surface area into this equation, we get: \[ r = \sqrt [\raise{7pt} \Large 3] ({ 3 \times 500 \over 4 \pi}) = \sqrt [\raise{7pt} \Large 3] ({ 1500 \over 4 \pi}) \]

This means that: \[ r = \sqrt[3] (119.3662...) \]

So if we work out the cube root: \[ r ≈ 4.924 \; cm \]

The diameter is equal to twice the radius.

This gives us a final answer of: \[ diameter = 4.924 \times 2 = 9.8 \; cm \; to \; 1 \; decimal \; place. \]