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

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