Mathematics 4024 · O Level · Surface area and volume
Surface area and volume — practice question
[Volume of cone $= \frac{1}{3}\pi r^2 h$]
[Curved surface area of a cone $= \pi r l$]
The sketch shows a gate post.
It is formed as a cylinder with a cone placed on top.
The cylinder and the cone each have diameter $8\,\text{cm}$.
The cylinder has height $95\,\text{cm}$ and the cone has height $15\,\text{cm}$.
(a)[3]
Calculate the volume of this gate post.
(b)[5]
Show that the gate post has a total curved surface area of $2580\,\text{cm}^2$, correct to 3 significant figures.
(c)[2]
A gate post that is geometrically similar has a total height of $150\,\text{cm}$.\nCalculate the total curved surface area of this gate post.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate cone volume” …