Question Video: Finding the Volume of a Cone | Nagwa Question Video: Finding the Volume of a Cone | Nagwa

Question Video: Finding the Volume of a Cone Mathematics • Second Year of Secondary School

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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 sketch of the cone. We are told that the diameter of the circular base is equal to 10.5. The height of the cone is 11.3. This is the perpendicular distance from the apex to the base. Note that the question does not tell us whether this is a right cone or an oblique one, but in fact it does not matter, since we have been given the perpendicular height. When using the perpendicular height, our formula for volume is applied in the same way to both cases.

In order to calculate the volume of any cone, we use the formula one-third 𝜋𝑟 squared multiplied by ℎ, where 𝑟 is the radius of the circular base. We know that the radius of any circle is half its diameter, and we are told the diameter is 10.5. The radius is, therefore, equal to a half multiplied by 10.5. This is equal to 5.25. We can now substitute our values for the radius and height into the formula.

The volume of the cone is 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 are asked to give our solution correct to two decimal places. As the deciding number is a six, we round up, giving us an answer of 326.16. Volume is measured in cubic units. And as there were no length units given for the diameter or the height, the volume is equal to 326.16 cubic units.

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