Mathematics 4024 · O Level · Surface area and volume

Surface area and volume — practice question

Volume of a cone $= \frac{1}{3}\pi r^2 h$. Curved surface area of a cone $= \pi r l$. A solid is made by removing a smaller cone from the middle of a larger cone. The small cone is mathematically similar to the large cone. The vertex of the large cone lies vertically below the vertex of the small cone. The height of the large cone is $21$ cm and the diameter of the top is $18$ cm. The height of the small cone is $14$ cm.
(a(i))[3]

Show that the solid has volume $399\pi\,\text{cm}^3$.

(a(ii))[6]

Calculate the overall surface area of the solid.

(b)[3]

A cylinder has height $13$ cm, correct to the nearest centimetre, and its base radius is $4.5$ cm, correct to the nearest $0.1$ centimetre. Calculate the upper bound of the volume, in $\text{cm}^3$, of the cylinder.

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