The diagram shows a solid object. It is made up of a cylinder with a hemisphere above it. The cylind

Question

The diagram shows a solid object. It is made up of a cylinder with a hemisphere above it. The cylinder has a radius of $x$ cm and a height of $y$ cm. The radius of the hemisphere is $2x$ cm. Express $y$ in terms of $x$ if the total volume of the solid is $72\pi$ $\text{cm}^3$.[2] Show that the total surface area, $A$ $\text{cm}^2$, of the solid is $144\pi\left(\frac{1}{x} + \frac{x^2}{108}\right)$.[2] Find the value of $x$ for which $A$ is a stationary value and determine the nature of the stationary value.[4]

Accepted Answer

(a) $y= \frac{72}{x^2} - \frac{16}{3}x$ (c) $x = 3.78$ ; Area is a minimum value

2024 GESS PRELIMS P2 Q9

2024 GESS PRELIMS P2 Q9