CAIE IGCSE Mathematics Core C5.4.1 Carry Out Calculations and Solve Problems Involving the Surface Area Questions

Choose the correct area or volume relationship in Core CAIE IGCSE Mathematics to calculate solid measures, recover missing dimensions and connect volumes with practical capacities.

Exam points

Calculate a cuboid volume with length × width × height, or use cross-sectional area × length for a triangular prism.
Substitute the radius and height into cylinder or sphere volume formulas, leaving an exact multiple of π when requested.
Add pairs of matching rectangular faces for a cuboid surface area, or use 4πr² for a sphere.
Recover a cube edge from its total surface area or volume using a square or cube root, then calculate the other measure if required.
Rearrange a cone volume formula to find an unknown radius, or equate sphere and cone volumes to find a height.
Convert a calculated cylindrical capacity from cubic metres to litres, applying 1000 litres per cubic metre.
Convert box and container dimensions to the same units before finding the whole number of cuboid boxes that fit.

[Maximum number: 6]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Core

The diagram shows the net of a cuboid.

[ 6 ]

(i)

Find the volume of the cuboid. $\mathrm{cm}^{3}$ [2]

[ 2 ]

120

M1 for $6\times4\times5$ oe.

(ii)

Show that the total surface area of the cuboid is $148 \mathrm{~cm}^{2}$ .

[ 2 ]

$2\times(6\times4+4\times5+6\times5)=148$
M1 for $6\times4$ , $4\times5$ or $6\times5$ oe soi.

(iii)

Calculate the total length of the edges of the cuboid.
cm [2]

[ 2 ]

60

M1 for $4\times6+4\times5+4\times4$ oe.

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CAIE IGCSE Mathematics Core C5.4.1 Carry Out Calculations and Solve Problems Involving the Surface Area Questions question 1

Question (a)

Question (i)

Question (ii)

Question (iii)