Question

PLEASE HELP FAST!

A cylinder and a cone have the same volume. The cylinder has radius x
and height y. The cone has radius 1/2x. Find the height of the cone in terms of y.

Answer 1

The height of the cone in terms of y is h = 12x⁴y

How to find the volume of a cone and cylinder?

The cylinder and the cone have the same volume.

Volume of a cylinder = πr²h

where

• r = radius
• h = height

Therefore,

Volume of a cylinder = πx²y

volume of a cone = 1 / 3 πr²h

where

• r = radius of the cone
• h = height of the cone

Therefore,

πx²y = 1 / 3 × π × (1 / 2x)² × h

πx²y = πh / 12x²

πx²y × 12x² / π = h

h = 12x⁴y

Therefore, the height of the cone in terms of y is h = 12x⁴y

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