Question

A cuboid has side lengths 3cm, 4cm and 7cm. A cylinder with a height double that of the longest side of the cuboid has the same volume. Calculate the radius and the surface area of the cylinder.

Answer 1

Explanation:

Longest side of cuboid: 7cm

Height of cylinder:

2 × 7 = 14 cm

Volume of cuboid:

7x3x4=84
`cm^3`

Volume of cylinder:

`84=14\pi r^2 \\r=\sqrt{(6)/(\pi) } \ \ \ cm\\r=1.38 \ cm\\`

Surface area of the cylinder:

`\pi r^2 + 2 \pi r h`

`6+2\pi (\sqrt{(6)/(\pi) } ) (14)`

=128 cm^2