Question

If the radius and height of a cylinder are increased by $10\%$ and decreased by $5\%$ respectively, then what will be the percentage change in volume? [4 MARKS]

Answer 1

Concept: 1 Mark
Formula: 1 Mark
Application: 2 Marks

Let the original radius be r and height be h.

New radius = 1.1r

New height = 0.95h

Volume
$=\pi r^{2}h$

New volume
$=\pi \times {\left(1.1r\right)}^2\times 0.95h$

$=1.1495\pi r^{2}h$

$\Rightarrow 14.95\%$ increase in volume.