CAIE IGCSE Mathematics Extended Compound Solid Mensuration

Practise calculating surface areas and volumes of compound or partial solids, including frustums, removed sectors and joined curved solids.

Exam points

calculate a frustum by subtracting the volume of a smaller similar cone or pyramid
add only exposed curved and flat surfaces when a cone, hemisphere or cylinder is joined
subtract removed solid volume or equate displaced volume to determine height or unused material

[Maximum number: 6]

Figure for Question E5.5.2 Carry out calculations and solve problems involving surface areas and question 1 — CAIE IGCSE Mathematics Extended

The diagram shows a horizontal container for water with a uniform cross-section. The cross-section is a semicircle.
The radius of the semicircle is 0.45 m and the length of the container is 4 m .

NOT TO SCALE

The greatest depth of the water in the container is $0.3\,\mathrm{m}$. The diagram shows the cross-section.
Calculate the number of litres of water in the container.
Give your answer correct to the nearest integer.

Figure for Answer to Question E5.5.2 Carry out calculations and solve problems involving surface areas and question 1 — CAIE IGCSE Mathematics Extended

742 or 743
M5 for a method leading to the volume of water, e.g.
$4\left\{2\times\frac{\operatorname{invcos}(0.15/0.45)}{360}\times\pi\times0.45^2-\frac12\times0.45^2\times\sin\left(2\operatorname{invcos}(0.15/0.45)\right)\right\}$
OR M2 for a correct sector area expression and M2 for a correct triangle area expression
If 0 scored, SC1 for $\operatorname{invcos}(0.15/0.45)$ , $\operatorname{invsin}(0.15/0.45)$ , or $\sqrt{0.45^2-0.15^2}$ soi

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E5.5.2 Carry out calculations and solve problems involving surface areas and question 1