Mathematics 4024 · O Level · Surface area and volume

Surface area and volume — practice question

The diagram depicts a regular pentagon $ABCDE$ with centre $O$.
(a)[3]

With $AB = 6\text{ cm}$ and $OA = d\text{ cm}$, show that $d = 5.10\text{ cm}$, correct to $2$ decimal places.

(b)[5]

[Volume of a pyramid $= \frac{1}{3} \times$ base area $\times$ height] The regular pentagon $ABCDE$ makes up the base of a pyramid. The vertex $F$ lies vertically above $O$. Each sloping edge of the pyramid measures $14\text{ cm}$. Calculate the volume of the pyramid.

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