Cambridge Essentials Mathematics Core 8 GM2 Consolidation Worksheet 1

/ GM2 Consolidation Worksheet 1

1 Area tells you the amount of space inside a flat shape. It is measured in square units.

Area of a rectangle = length × width

Calculate the area of each rectangle.

a b

2 Area of a triangle = (base × height) ÷ 2

Calculate the area of each triangle.

a b

3 Volume measures the total space inside a three-dimensional (3-D) shape.

Volume is always measured in cubic units.

A cubic centimetre is a cube that is
1 cm long, 1 cm wide and 1 cm high.
This cube has a volume of 1 cm3.

Volume of a cuboid = length × width × height

Calculate the volume of each cuboid.

a b c

4 An 8 cm cube is not the same as a shape that has a volume of 8 cm3.

An 8 cm cube is a cube with length, width and height each 8 cm.
Its volume is 8 cm × 8 cm × 8 cm = 512 cm3.

Look at this cuboid.
Its volume is 4 cm × 2 cm × 1 cm = 8 cm3.

a What is the side length of a cube with volume 8 cm3?

b Draw a different cuboid with volume 8 cm3.
Mark the length of each edge.

5 Surface area is the total area of all the faces of the shape.

A cuboid has six faces. Top and bottom have the same area.

Front and back have the same area. The two sides have the same area.

a Find the surface area of these cuboids.

A B

b A net of a 3-D shape is a 2-D shape that can be folded to make the 3-D shape.
The surface area is also the area of the net.

This is a net for cuboid A.

i What is the length QR?
ii What is the length TU?
iii Work out the total area of the net.
iv Does your answer match part a?

c i Draw a net of cuboid B. Label the faces and show the edge lengths.

ii Find the surface area. Check that it matches your answer to part a.