Question Video: Finding the Volume of a Cylinder Where the Answer Is Given in Terms of Pi Mathematics • 8th Grade

A cylinder has a radius of 9 cm and a height of 14 cm. Work out the volume of the cylinder, giving your answer in terms of 𝜋.

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Video Transcript

A cylinder has a radius of nine centimeters and a height of 14 centimeters. Work out the volume of the cylinder, giving your answer in terms of 𝜋.

Let’s begin by recalling how we calculate the volume of a cylinder. The formula we use is 𝜋𝑟 squared ℎ, where 𝑟 represents the radius and ℎ the height of the cylinder. In applying this formula, we’re calculating the area of the cylinder’s circular cross section, and then multiplying this by its height.

We’re given that the radius of this cylinder is nine centimeters and the height is 14 centimeters, so we can substitute both values into the formula. Doing so gives that the volume is equal to 𝜋 multiplied by nine squared multiplied by 14.

Now, we could type this into a calculator and evaluate the answer as a decimal, but the question specifies that we should give our answer in terms of 𝜋. So instead, we’ll just evaluate nine squared multiplied by 14. Nine squared is 81, and 81 multiplied by 14 is 1,134. The volume of the cylinder is 1,134𝜋 cubic centimeters.