A solid prism has an equilateral triangle as its horizontal base, with side $x$ cm. The prism’s side faces are vertical. Its height is $h$ cm and its volume is $2000\text{ cm}^3$.
(i)[3]
Write $h$ in terms of $x$ and show that the prism’s total surface area, $A\text{ cm}^2$, can be written as $A = \frac{\sqrt{3}}{2}x^2 + \frac{24000}{\sqrt{3}}x^{-1}$.
(ii)[3]
Since $x$ may change, find the value of $x$ for which $A$ is stationary.
(iii)[2]
Determine the nature of this stationary value, showing all the working needed.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the prism volume formula to obtain $h=\dfrac{8000}{\sqrt3x^2}$” …