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Video: Finding the Volume of a Cylinder Given a Diameter

Kathryn Kingham

Work out the volume of the cylinder, giving your answer accurate to two decimal places.<Figure>

02:41

Video Transcript

Work out the volume of the cylinder, giving your answer accurate to two decimal places.

To find the volume of a cylinder, we multiply the area of the base times the height. The space shaded in pink here is one of the bases of the cylinder. Cylinders have two circular bases, and to find the volume, we first need to find the area of the circles. The height of a cylinder is the space between the two bases; you can see that in green here.

Because the space is a circle, we would use the formula for finding the area of a circle to find out what the area of this base is. And the formula for finding the area of a circle is 𝜋𝑟 squared. This formula will help us find the volume of the given cylinder.

Let’s start by finding out the radius of the base. The radius is the distance from the center of the circle to any point on the outside. The radius is also half of the diameter.

We’re given the diameter of the circle and the radius would be half of that. The radius here would be seven centimeters. The height of the cylinder is also given to us, height 13 centimeters.

Our next step will be to multiply all of these things out. If I multiply seven squared times pi times 13. I’ve entered this into my calculator to get the most accurate answer, and it tells me that two 2001.19452, on and on, is the answer.

I wanna give the accurate answer up to two decimal places, so I round to the hundredths. And that gives me 2001.19, but it’s really important that I don’t miss the units. We’re talking about centimeters. And when we deal with volume, it’s always a cubed unit, our final answer here being 2001.19 centimeters cubed.