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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.

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

Key stage:  KS 2

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   3D Shapes

Difficulty level:  

Worksheet Overview

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

CORRECT ANSWER
Volume
  • Question 2

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

D = 3a + 2b - c

CORRECT ANSWER
Length
  • Question 3

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

D = 3ab

CORRECT ANSWER
Area
  • Question 4

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

A = πr2

CORRECT ANSWER
Area
  • Question 5

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

V = πr2h

CORRECT ANSWER
Volume
  • Question 6

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

S = πr2+ 2πrh

CORRECT ANSWER
Area
  • Question 7

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

CORRECT ANSWER
4πr2
  • Question 8

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

CORRECT ANSWER
4/3πr3
  • Question 9

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

CORRECT ANSWER
2πr
  • Question 10

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

CORRECT ANSWER
3r
---- OR ----

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