CAIE IGCSE Mathematics Extended E5.4.1 Carry Out Calculations and Solve Problems Involving the Surface Area 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: 6]

(a)

NOT TO SCALE

The diagram shows a cylinder with radius 8 cm inside a sphere with radius 17 cm . Both ends of the cylinder touch the curved surface of the sphere.

[ 6 ]

(i)

Show that the height of the cylinder is 30 cm .

[ 2 ]

$2\sqrt{17^2-8^2}$ or $\sqrt{34^2-16^2}$ oe
M1 for $17^2=8^2+d^2$ or $34^2=16^2+k^2$

(ii)

Calculate the volume of the cylinder as a percentage of the volume of the sphere.
[The volume, V, of a sphere with radius r is V=4/3 r^3.]

[ 4 ]

29.3 or 29.30 to 29.31
M3 for $\frac{\pi\times8^2\times30}{\frac43\pi\times17^3}\times100$ oe
OR M1 for $\pi\times8^2\times30$ oe
M1 for $\frac43\pi\times17^3$ oe

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CAIE IGCSE Mathematics Extended E5.4.1 Carry Out Calculations and Solve Problems Involving the Surface Area Questions question 1

Question (a)

Question (i)

Question (ii)