A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The cone is tilted at an angle so its peak touches the edge of the cylinder's base. What is the volume of the space remaining in the cylinder after the cone is placed inside it?

Question

Cherish Ho

Mathematics

11 December, 12:55

A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The cone is tilted at an angle so its peak touches the edge of the cylinder's base. What is the volume of the space remaining in the cylinder after the cone is placed inside it?

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Answers (1)

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Ashlyn Fitzpatrick · Answer 1

Volume of cylinder = pi x r^2 x h

Volume of cone = 1/3 x pi x r^2 x h

radius of cone = 1/2 (r)

Remaining volume = Volume of cylinder - Volume of cone

= pi x r^2 x h - 1/3 x pi x (r/2) ^2 x h

= pi r^2 h - 1/4 pi r^2 h

= 3/4 (pi r^2 h)