Home / iGCSE Mathematics (0580) :E5.5 Carry out calculations involving the areas and volumes of compound shapes.iGCSE Style Questions Paper 2

iGCSE Mathematics (0580) :E5.5 Carry out calculations involving the areas and volumes of compound shapes.iGCSE Style Questions Paper 2

Question

The diagram shows a circular disc with radius 6 cm.
In the centre of the disc there is a circular hole with radius 0.5 cm.
Calculate the area of the shaded section.

Answer/Explanation

Ans: 112 or 112.3 to 112.33

Question


The diagram shows a cube of side length 8cm.
(a) Calculate the length of the diagonal BS.
BS = ………………………………….. cm
(b) Calculate angle SBD.
Angle SBD = …………………………………………

Answer/Explanation

Ans:

(a) 13.9 or 13.85 to 13.86
(b) 35.1 to 35.5[4…]

Question



ABCD is a kite.
The diagonals AC and BD intersect at X.
AC = 12cm, BD = 20cm and DX:XB = 3:2 .
(a) Calculate angle ABC.
(b) Calculate the area of the kite.

Answer/Explanation

Ans:

(a) 73.7 or 73.73 to 73.74

(b) 120

Question

The diagram shows a rectangle ABCE.
D lies on EC.
DAB is a sector of a circle radius 8cm and sector angle 30°.
Calculate the area of the shaded region.

Answer/Explanation

Ans: 1.38 or 1.39 or 1.384 to 1.389 

Question

The base of a rectangular tank is 1.2 metres by 0.9 metres.
The water in the tank is 53 centimetres deep.
Calculate the number of litres of water in the tank.

Answer/Explanation

Ans: 572.4 

Question



The diagram shows a rectangular garden divided into different areas.
FG is the perpendicular bisector of BC.
The arc HJ has centre D and radius 20m.
CE is the bisector of angle DCB.
Write down two more statements using loci to describe the shaded region inside the garden.
The shaded region is
• nearer to C than to B
• ……………………………………………………………………………………………………………………………………
• ……………………………………………………………………………………………………………………………………

Answer/Explanation

Ans:

More than 20m from D oe
Nearer to CD than to CB oe

Question

The scale on a map is 1 : 20 000.
The area of a lake on the map is 1.6 square centimetres.
Calculate the actual area of the lake.
Give your answer in square metres.
…………………….. \(m^2\)

Answer/Explanation

Ans:

64 000

Question

A company makes solid chocolate eggs and their shapes are mathematically similar.
The diagram shows eggs of height 2 cm and 6 cm.
The mass of the small egg is 4 g.
Calculate the mass of the large egg..

Answer/Explanation

Since, the eggs are similar in shapes

So ratio of their heights are 2:6 = 1:3 

Also ratio of their volumes are 1:27

Since,eggs are mathematically similar, So, their volumes are proportional to the cube of their heigths 

So, Let the mass of larger egg be M.

Therefore, \((6cm\div 2cm)^3\)=\(M\div 4g\)

Simplifying , 

\(3^3=M\div 4g\)

M= 27. 4g

M= 108g

Question

                           

The top of a desk is made from a rectangle and a quarter circle. The rectangle measures 0.8m by 1.4m. Calculate the surface area of the top of the desk.

▶️Answer/Explanation

1.62

Question

                     

The diagram represents a rectangular gate measuring 1.5m by 3.5m. It is made from eight lengths of wood. Calculate the total length of wood needed to make the gate.

▶️Answer/Explanation

24.3(0788…)

Question

A semicircle of diameter 6 cm is cut from a rectangle with sides 6 cm and 8 cm.
Calculate the perimeter of the shaded shape, correct to 1 decimal place.

▶️Answer/Explanation

31.4 cao

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