A cylinder has a radius of $r$ cm and a height of 10 cm - Junior Cycle Mathematics - Question 14 - 2019

Since 10% of the volume is lost during the process, the volume of the cone $V_{cone}$ is: $V_{cone} = 0.90 imes V_c = 0.90 imes 10 ext{cm} imes \\pi r^2 = 9 ext{cm} imes \\pi r^2$

The volume $V_{cone}$ of a cone is given by: V_{cone} = rac{1}{3} imes ext{Base Area} imes ext{Height} = \frac{1}{3} imes \\pi r^2 imes h

Setting the two volume expressions equal gives: $9 ext{cm} imes \\pi r^2 = \frac{1}{3} imes \\pi r^2 imes h$

We can cancel out $\ ext{cm} imes \\pi r^2$ (assuming $r > 0$): $9 = \frac{1}{3} h$

Multiplying both sides by 3 yields: $h = 27 ext{ cm}$

The original height of the cylinder was 10 cm. The new height of the cone is 27 cm.

The increase in height is: $Increase = h - 10 = 27 - 10 = 17 ext{ cm}$

To find the percentage increase: $ext{Percentage Increase} = \frac{Increase}{Original Height} \times 100 = \frac{17}{10} \times 100 = 170\%$