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

Step-by-step explanation:

Longest side of cuboid: 7cm

Height of cylinder:

2 × 7 = 14 cm

Volume of cuboid:

7x3x4=84$cm^3$

Volume of cylinder:

$84=14\pi r^2 \\r=\sqrt{\frac{6}{\pi} } \ \ \ cm\\r=1.38 \ cm$

Surface area of the cylinder:

$\pi r^2 + 2 \pi r h$

$6+2\pi (\sqrt{\frac{6}{\pi} } ) (14)$

=128 cm^2