Question Video: Finding the Volume of a Cone Mathematics • 8th Grade

Work out the volume of a cone with a diameter of 10.5 and a height of 11.3. Give your solution to two decimal places.

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Video Transcript

Work out the volume of a cone with a diameter of 10.5 and a height of 11.3. Give your solution to two decimal places.

Let’s begin by drawing a diagram of the cone. We’re told that the diameter is 10.5. This is a distance from one side of the circular base to the other, passing through the centre. The height of the cone is equal to 11.3. This is the distance from the apex or top of the cone to the centre of the base. In order to calculate the volume of a cone, we use the formula one-third 𝜋𝑟 squared multiplied by ℎ. At this stage, we know the height of the cone, but we don’t know the radius.

The radius of the circular base is the distance from the centre to the circumference of the circle. This is equal to half of the diameter. Therefore, to calculate the radius, we divide 10.5 by two. This is equal to 5.25. And we now have values for the radius and height of the cone. Substituting in these values gives us a volume equal to one-third multiplied by 𝜋 multiplied by 5.25 squared multiplied by 11.3. Typing this into the calculator gives us 326.1562 and so on. We were asked to round our solution to two decimal places. As the six in the thousandths column is greater than five, we will round up to 326.16. Volume is measured in cubic units. As there are no specific units in this question, the volume of the cone is equal to 326.16 cubic units.

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