Video: Finding the Volume of a Cone given Its Height and Its Base Perimeter

Determine, to the nearest tenth, the volume of a right cone having a height of 106 cm, given that the perimeter of its base is 318 cm. Use πœ‹ = 22/7.

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Video Transcript

Determine, to the nearest tenth, the volume of a right cone having a height of 106 centimetres, given that the perimeter of its base is 318 centimetres. Use πœ‹ equal to 22 over seven.

The cone in this question has a height of 106 centimetres. This is the distance from the apex to the centre of the circular base. The perimeter of the base is 318 centimetres. As the base is a circle, this is the circumference of the circle. We’re asked to calculate the volume of the cone. This is equal to one-third πœ‹π‘Ÿ squared multiplied by the height.

At present, we know the height of the cone, but we don’t know its radius. We recall that the circumference of a circle is equal to two πœ‹π‘Ÿ. This means that 318 is equal to two πœ‹π‘Ÿ. As we’re told to use πœ‹ as 22 over seven, 318 is equal to two multiplied by 22 over seven multiplied by π‘Ÿ. The right-hand side of our equation simplifies to 44 over seven π‘Ÿ. Dividing both sides by 44 over seven gives us π‘Ÿ is equal to 1113 over 22. We can now substitute this value along with the height into our formula for the volume of a cone. The volume is equal to one-third multiplied by 22 over seven multiplied by 1113 over 22 squared multiplied by 106. Typing this into the calculator gives us 284219.727 and so on.

We’re asked to give our answer to the nearest tenth. Therefore, the deciding number is the two in the hundredths column. As this is less than five, we round down. The volume of a right cone with height 106 centimetres and base circumference of 318 centimetres is 284219.7 cubic centimetres. Note that our units here are cubed as we’re dealing with volume.

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