Mathematics 0580 · IGCSE · Surface area and volume

Surface area and volume — practice question

ABCDEFGH is a regular octagon with side length $6$ cm. The diagram displays only part of the octagon. $O$ denotes the centre of the octagon and $M$ is the midpoint of $AB$.
(a(i)(a))[2]

Show that angle $OAM$ is $67.5\degree$.

(a(i)(b))[4]

Calculate the area enclosed by the octagon.

(a(ii))[3]

Find the area of the circle passing through the vertices of the octagon.

(b(i))[2]

Calculate the volume of the container.

(b(ii))[6]

Calculate how many litres of water the container holds. Give your answer correct to the nearest integer.

Worked solution & mark scheme

This 17-mark question has a full step-by-step worked solution and mark scheme. One marking point: M1 for $(8 - 2) \times 180 / 8$ or $360 / 8$ or $(2 \times 8 - 4) \times 90 / 8$

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