Page 178 - MAT KS3 Y8 Cambridge CheckPoint

17.6 Using nets of solids to work out surface areas

2 This is part of Dakarai’s homework.
Dakarai has made several mistakes.
a Explain the mistakes that Dakarai has made.
b Work out the correct answer for him.
b Work out the correct answer for him.

Question Work out the 3.2 cm
surface area of 4 cm
this prism.
2 cm
15 mm
6 cm
6.8 cm

Answer Area A = 2 × 6.8 = 13.6 cm 2
Area B = 6 × 6.8 = 40.8 cm 2
Area C = 4 × 6.8 = 27.2 cm 2
Area D = 3.2 × 6.8 = 21.76 cm 2
Area E = 1 × (3.2 + 6) × 15
2
= 1 × 9.2 × 15 = 69 cm 2
2
Area F = area E
Total surface area = 13.6 + 40.8 + 27.2 + 21.76 + 69 = 172.36 cm 2

3 Mia draws a cube of side length 48 mm.
She also draws a triangular prism with the 4.2 cm
dimensions shown.
Mia thinks that the cube and the triangular 48 mm 3 cm
12.7 cm
prism have the same surface area.
3 cm
Is Mia correct? Show clearly how you worked
out your answer.

Summary

You should now know that: You should be able to:
The formula for the circumference of a circle is Know the definition of a circle and the names of
C = πd or C = 2πr. its parts.
The formula for the area of a circle is A = πr . Know and use formulae for the circumference and area
2
The formula for the area of a triangle is A = 1 2 bh. of a circle.
The formula for the area of a parallelogram is Derive and use formulae for the area of a triangle,
parallelogram and trapezium.
A = bh.
The formula for the area of a trapezium is Calculate areas of compound shapes.
A = 1 2 × (a + b) × h. Calculate lengths, surface areas and volumes of cuboids.
The formulae for the volume and surface area of a cuboid Use simple nets of solids to work out their surface
are V = lwh and SA = 2lw + 2lh + 2wh. areas.

176 17 Area, perimeter and volume
176