Question

A cylinder has a volume of 60cm what is the volume of a cone with the same radius and height.

Answer 1

20 cm³

Explanation:

Since the volume of a cylinder is 60 cm³, which we can express it as:

`\displaystyle \large{\pi r^2 h=60}`

Keep in mind that
`\displaystyle \large{\pi r^2 h}` is the cylinder’s volume formula, and we want to find the volume of a cone with same radius and height. When they say same radius and height, they mean that the radius and height are the same as cylinders’.

But since no values of radius and height are given, we know that the volume of a cone is:

`\displaystyle \large{(1)/(3)\pi r^2 h}`

Compare both formulas:

`\displaystyle \large{\pi r^2h}` — cylinder’s volume

`\displaystyle \large{(1)/(3)\pi r^2h}` — cone’s volume

See how they are quite similar except that cone’s volume has 1/3. That means cone’s volume is 1/3 of cylinder’s volume

Finding cone’s volume, multiply both sides by 1/3:

`\displaystyle \large{\pi r^2h=60}\\\displaystyle \large{(1)/(3)\pi r^2h=(1)/(3)\cdot 60}\\\displaystyle \large{(1)/(3)\pi r^2h=20}`

Therefore, the volume of a cone with same radius and height from cylinder is 20 cm³.

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Summary

Volume (Cone) (1/3 of cylinder’s volume):

`\displaystyle \large{V=(1)/(3)\pi r^2 h}`

Volume (Cylinder):

`\displaystyle \large{V=\pi r^2h}`

They are quite related!

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Others

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