 # One-, Two- and Three-Dimensional Formula: Which is It?

In this worksheet, students decide whether a given formula is one-dimensional, two-dimensional or three-dimensional. Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Use Standard Mathematical Formulae

Difficulty level:   ### QUESTION 1 of 10

By analysing the dimensions to the right of the equals sign, we can easily say whether a formula could be for length, area or volume.

A formula for length can only be one-dimensional.

This means that lengths occur on their own e.g. C = 3d or P = a + 2b

A formula for area can only be two-dimensional.

This means that lengths occur in pairs e.g. A = 3ab or A = a2 + 2ab

A formula for volume can only be three-dimensional.

This means that lengths occur in threes e.g. C = 5d3 or P = abc + 2a2b

Look at the following formula and state whether it could represent length, area or volume:

D = abc

Length

Area

Volume

Look at the following formula and state whether it could represent length, area or volume:

D = 3a + 2b - c

Length

Area

Volume

Look at the following formula and state whether it could represent length, area or volume:

D = 3ab

Length

Area

Volume

Look at the following formula and state whether it could represent length, area or volume:

A = πr2

Length

Area

Volume

Look at the following formula and state whether it could represent length, area or volume:

V = πr2h

Length

Area

Volume

Look at the following formula and state whether it could represent length, area or volume:

S = πr2+ 2πrh

Length

Area

Volume

Which of these expressions will work out the surface area of a sphere?

πr

4πr3

4πr2

Which of these expressions will work out the volume of a sphere?

4/3πr

4/3πr2

4/3πr3

Which of these expressions will work out the circumference of a circle?

2πr

2πr2

2πr3

Which of these expressions could not be an expression for a volume?

3r

2πr2h + 3rh2

2πr3

• Question 1

Look at the following formula and state whether it could represent length, area or volume:

D = abc

Volume
• Question 2

Look at the following formula and state whether it could represent length, area or volume:

D = 3a + 2b - c

Length
• Question 3

Look at the following formula and state whether it could represent length, area or volume:

D = 3ab

Area
• Question 4

Look at the following formula and state whether it could represent length, area or volume:

A = πr2

Area
• Question 5

Look at the following formula and state whether it could represent length, area or volume:

V = πr2h

Volume
• Question 6

Look at the following formula and state whether it could represent length, area or volume:

S = πr2+ 2πrh

Area
• Question 7

Which of these expressions will work out the surface area of a sphere?

4πr2
• Question 8

Which of these expressions will work out the volume of a sphere?

4/3πr3
• Question 9

Which of these expressions will work out the circumference of a circle?

2πr
• Question 10

Which of these expressions could not be an expression for a volume?

3r
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