Question

The radius of the base and height of a right circular cylinder are each increased by 20%. The volume of the cylinder will be increased by:

(a) 40%

(b) 60%

(c) 72.8%

(d) 96%

Answer 1

Correct option is (c) 72.8%

Volume = πr²h

new radius = r + \(\frac{20}{100}\)r

= \(\frac 56\)r

So

\(= h + \frac{20}{100}h\)

\(= \frac 65 h\)

Volume = π\(\left(\frac {6r}5\right)^2 \left(\frac 65h\right)\)

\(= \frac{216}{125} \pi r^2 h\)

∴  Increase in volume = \( \frac{216}{125} \pi r^2 h\)