Volume of a Cone Calculator

Volume of a Cone Example 1

Find the volume of the cone below. Give your answer to 1 decimal place.

The height of the cone is 12 cm. The radius is 4 cm.

The formula for the volume of a closed cone is: \[ V = {1 \over 3} \pi r^2 h \]

If we substitute the values of the radius and height into the formala, we get: \[ V = {1 \over 3} \pi \cdot 4^2 \cdot 12 \]

If we simplify this, we get: \[ V = {1 \over 3} \pi \cdot 16 \cdot 12 = {1 \over 3} \pi \cdot 192 = 64 \pi\]

This gives us a final answer of: \[ V = 201.1 \;\ cm^3 \;\ to \;\ 1 \;\ decimal \;\ place \]

Volume of a Cone Example 2

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

The cone is lying on its side. The actual height of the cone is 10 inches. The radius is 4 ½ inches.

The formula for the volume of a closed cone is: \[ V = {1 \over 3} \pi r^2 h \]

If we substitute the values of the radius and height into the formala, we get: \[ V = {1 \over 3} \pi \cdot (4{ 1 \over 2})^2 \cdot 10 \]

If we simplify this, we get: \[ V = {1 \over 3} \pi \cdot {81 \over 4} \cdot 10 = {1 \over 3} \pi \cdot {405 \over 2} = {135 \over 2} \pi \]

This gives us a final answer of: \[ V = 212.1 \;\ in^3 \;\ to \;\ 1 \;\ decimal \;\ place \]

Volume of a Cone Example 3

Find the volume of the cone below to 2 decimal places.

The height of the cone is 4.8 meters. The diameter of the cone is 4.6 meters.

To find the radius, we divide the diameter by 2. So the radius = 4.8 ÷ 2 = 2.4 meters.

The formula for the volume of a closed cone is: \[ V = {1 \over 3} \pi r^2 h \]

If we substitute the values of the radius and height into the formala, we get: \[ V = {1 \over 3} \pi \cdot (2.3)^2 \cdot 4.8 \]

If we simplify this, we get: \[ V = {1 \over 3} \pi \cdot 5.29 \cdot 4.8 = {1 \over 3} \pi \cdot 25.392 = 8.464 \pi \]

This gives us a final answer of: \[ V = 26.59 \;\ m^3 \;\ to \;\ 2 \;\ decimal \;\ places \]

Volume of a Cone Example 4

Find the volume of the witch's black hat shown below. Give your answer to the nearest cm³.

The height of the cone is 62 cm. The diameter of the cone is 18 cm.

To find the radius, we divide the diameter by 2. So the radius = 18 ÷ 2 = 9 cm.

The formula for the volume of a closed cone is: \[ V = {1 \over 3} \pi r^2 h \]

If we substitute the values of the radius and height into the formala, we get: \[ V = {1 \over 3} \pi \cdot 9^2 \cdot 62 \]

If we simplify this, we get: \[ V = {1 \over 3} \pi \cdot 81 \cdot 62 = {1 \over 3} \pi \cdot 5022 = 1674 \pi \]

This gives us a final answer of: \[ V = 5259 \;\ cm^3 \;\ to \;\ the \;\ nearest \;\ cm^3 \]