Initial Diagnostic Audit - Unit C4: Volumes

Do NOT use a calculator for any questions in the audit unless specifically told otherwise
Section C4.1 - Volumes of Cubes, Cuboids, Cylinders and Prisms
FORMULAE

The volume of a cube is given by
V = a3
where a is the length of each side of the cube.
The volume of a cuboid is given by
V = abc
where a, b and c are the lengths shown in the diagram.
The volume of a cylinder is given by
V = πr2h
where r is the radius of the cylinder and h is its height.

What is the volume of

1. a cube of side length 4 cm    V = cm3
2. a cuboid of side lengths 3 cm, 4 cm and 5 cm    V = cm3
3. a cylinder of height 8 cm and radius 3 cm3    V = cm2
4. The volume of a cube is 150 cm3. What is the length of each side, to 2 decimal places?
Length = cm
5. The volume of a cuboid is 80 cm3. Two of the sides are each of length 4 cm.
What is the length of the third side?    Length = cm
Section C4.2 - Mass, Volume and Density
FORMULAE

Density = Mass ÷ Volume

The density of water is 1 g/cm3 or 1000 kg/m3

6. What is the mass of water in a tank measuring 25 cm × 40 cm × 50 cm?
Mass = kg
7. A bottle holds 450 cm3 of water and has a total mass of 530 g when full.

(a) What is the mass of the water in the bottle?    Mass = g

(b) What is the mass of the empty bottle?    Mass = g

8. A rectangular block of metal with dimensions 5 cm × 10 cm × 50 cm has a mass of 800 g.

(a) What is the block's density in g/cm3?    Density = g/cm3

(b) What is the block's density in kg/m3?    Density = kg/m3

Section C4.3 - Volumes of Pyramids, Cones and Spheres

You may use a calculator for questions in this section

FORMULAE

The volumes of a pyramid, a cone and a sphere are found using the following formulae;

Pyramid
Cone
Sphere
V =  
1
Ah
3
V =  
1
 πr2h
3
V =  
4
 πr3
3
9. What is the volume of a sphere of radius 5 cm? Give your answer to the nearest whole number.
Volume = cm3
10. What is the volume of a cone of height 10 cm and radius 3 cm?
Volume = π cm3
11. What is the volume of a square-based pyramid with base lengths 5 cm and height 18 cm?
Volume = cm3
12. The volume of a small ball is 450 cm3. What is the radius of the ball? Give your answer to 2 decimal places.
Radius = cm
13. The surface area of a sphere is 64π cm2. What is the volume of the sphere?
Volume =  
  π cm2
Section C4.4 - Dimensions
14. A: a + b + c B: (ab)2 C: a2b + ab2
D: (a + c)2 E: (abc)3

Which of the formulae above, where a, b and c are lengths, could be

(a) a perimeter?

(b) an area?

(c) a volume?

15. The table below shows some expressions.
a, b, c and d represent lengths.
π and 3 are numbers which have no dimensions.

A:  
πab3
   
3d
B: πbc
C: ac + bd
 
D: π(a +b)
 
E: 3(c + d)3
F: 3πbc2

Select the two expressions that could represent areas.

Marking your audit and producing your report

Once you are happy you have completed the audit, click the button below to mark your audit.
You will not be able to mark the audit again once you have clicked this button.
Mark your answers.

Now you can click the button below to produce your report. This button can be used more than once.
Produce your report.

< Back to Unit Menu
Produced by Russell Geach for CIMT - January 2013