Mathematics

Mathematics

Problem

A right circular cylinder has radius 7 cm7\,\text{cm} and contains 6160 cm36160\,\text{cm}^3 of water. Calculate the height of the cylinder, correct to the nearest millimetre.
Intuitive explanation

The volume of a cylinder is the product of its base area and height—so if you know the volume and radius, you can rearrange V=πr2hV = \pi r^2 h to solve for the missing height. This is a straightforward algebraic rearrangement: divide both sides by πr2\pi r^2 to isolate hh, then substitute the given numbers carefully, keeping track of units as you convert to millimetres.

Intuitive explanation

The volume of a cylinder is the product of its base area and height—so if you know the volume and radius, you can rearrange V=πr2hV = \pi r^2 h to solve for the missing height. This is a straightforward algebraic rearrangement: divide both sides by πr2\pi r^2 to isolate hh, then substitute the given numbers carefully, keeping track of units as you convert to millimetres.

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