CAIE IGCSE Mathematics Extended E5.5.2 Carry Out Calculations and Solve Problems Involving Surface Areas and Questions

Practise Extended CAIE IGCSE Mathematics by decomposing solids into faces and combining their component areas.

Exam points

Calculate surface area of cuboids, prisms and other solids from their faces.
Use nets, rectangles, triangles and circles to find total surface area.
Apply consistent units and combine component areas accurately.

[Maximum number: 4]

NOT TO SCALE

The diagram shows a frustum made by removing a small cone from a large cone.
The height of the small cone is 7.5 cm .
The height of the frustum is 4.5 cm .
The radius of the large cone is 4.2 cm .
Work out the volume of the frustum.

168 or 167.5 to 167.6

M3 for
$\frac{\pi}{3} \times\left[4.2^{2} \times(4.5+7.5)-\left(4.2 \times \frac{7.5}{4.5+7.5}\right)^{2} \times 7.5\right]$
oe
or M2 for
$\left(\frac{7.5}{7.5+4.5}\right)^{3} \times \frac{1}{3} \times \pi \times 4.2^{2} \times(4.5+7.5)$
or for $\frac{1}{3} \times \pi \times\left(4.2 \times \frac{7.5}{4.5+7.5}\right)^{2} \times 7.5$
or $\mathbf{M 1}$ for $\frac{1}{3} \times \pi \times 4.2^{2} \times(4.5+7.5)$
OR
M1 for $\frac{1}{3} \times \pi \times 4.2^{2} \times(4.5+7.5)$
M1 for $\frac{4.2}{4.5+7.5}=\frac{\text { radius }}{7.5}$ oe or better
M1 for $\frac{1}{3} \times \pi \times(\text { their } 2.625)^{2} \times 7.5$

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CAIE IGCSE Mathematics Extended E5.5.2 Carry Out Calculations and Solve Problems Involving Surface Areas and Questions question 1