The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Find Pressure, Force and Area

In this worksheet, students will practise using the Force, Pressure, Area formulae pyramid to find the correct single formula to apply to find a missing variable.

'Find Pressure, Force and Area' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change, Mensuration

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Units and Measurement

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

While speed, distance and time are the most common compound unit questions to see on exams, you will still need to be able to calculate others too. 

In this activity, we will focus on calculating pressure, force and area.

 

The most challenging element when completing questions about pressure, force and area is remembering the correct formula to apply in each case. 

 

 

How to Remember the Formulae 

The easiest way to do this is to memorise the formulae triangle shown below, which we can then use to find each individual formula we need to use: 

 

 

 

How To Use This Diagram

It's quite simple, just highlight the element you are seeking (we've done it with a red circle below) and the formula to use will be constructed using the two remaining elements. 

 

 

Let's look at this formulae in action now in some examples.

 

 

 

e.g What is the pressure when a force of 8 N is applied to an area of 2 m2?

 

The first step in these calculations is always to decide what we need to find out.

In this case, we are directly asked for the to find pressure, so we need to use this formula:

P = F ÷ A

 

Now we can simply plug our numbers from the question into this formula:

P = 8 ÷ 2

 

The last question that we need to ask ourselves is which units to use with our answer.

Pressure here could be given in N/m2, but could also be given in Pascals (Pa).

These are both viable options and you will get marks either way.

 

So Pressure = 4 Pa or 4 N/m2

 

 

 

e.g. The pressure on an object is 3 Pa and the force being applied is 15 N. What is the area on which the force is acting?

 

Once again, we need to decide which formula to use: 

A = F ÷ P

 

Plugging in our numbers gives us:

A = 15 ÷ 3 = 5

 

When you are dealing with pressure, force and area, unless you are told otherwise, the units to use will be m2.

 

So Area = 5 m2

 

 

 

In this activity, we will use the Force, Pressure, Area formulae pyramid to find the correct single formula to apply to find a missing variable using the method shown above. 

Type two words in the spaces to complete the sentence below. 

A force of 12 N acts on an area of 3 m2.

 

 

What is the average pressure which is exerted on this area?

4 Pa

36 Pa

15 Pa

Find the average pressure for a force of 10 N acting over an area of 2 m2.

 

Type your answer as a number without a unit in the box below, as this has already been provided for you. 

4 Pa

36 Pa

15 Pa

Type two words in the spaces to complete the sentence below.

4 Pa

36 Pa

15 Pa

A 2 m2 object has a pressure applied to it of 7 Pa.

 

What is the force being exerted on this object?

9 N

3.5 N

14 N

Find the force acting on a 3 m2 object with a pressure of 9 Pa being applied. 

 

Type your answer as a number without a unit in the box below, as this has already been provided for you. 

9 N

3.5 N

14 N

Type two words in the spaces to complete the sentence below. 

9 N

3.5 N

14 N

A force of 3 N produces a pressure of 3 Pa.

 

What is the area being affected by this pressure and force?

9 m2

1 m2

6 m2

A pressure of 4 Pa is produced by a force of 10 N.

 

What area does this force act over? 

 

Type your answer as a number without a unit in the box below, as this has already been provided for you. 

9 m2

1 m2

6 m2

Match each force and volume on the left with its corresponding pressure on the right. 

Column A

Column B

F = 15 N , A = 3 m2
P = 0.5 Pa
F = 15 N , A = 0.5 m2
P = 30 Pa
F = 2 N , A = 4 m2
P = 5 Pa
F = 1 N , A = 0.1 m2
P = 10 Pa
  • Question 1

Type two words in the spaces to complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
Remember that we need to look at our formulae pyramid and cover up the variable we are seeking. If we cover Pressure, then we are left with: Pressure = Force ÷ Area As with any division sum, it is essential to get these two elements the right way round or we will not reach the correct answer.
  • Question 2

A force of 12 N acts on an area of 3 m2.

 

 

What is the average pressure which is exerted on this area?

CORRECT ANSWER
4 Pa
EDDIE SAYS
It's all about identifying the correct formula to use in these cases. We are looking for pressure so if we cover this in our pyramid, we are left with the formula: Pressure = Force ÷ Area Now we just need to substitute our values into this formula: Pressure = 12 ÷ 3 Pressure = 4 Pa or N/m2
  • Question 3

Find the average pressure for a force of 10 N acting over an area of 2 m2.

 

Type your answer as a number without a unit in the box below, as this has already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
We are seeking pressure again here, so we need to use the same formula as the previous question: Pressure = Force ÷ Area Now we just need to substitute our values into this formula: Pressure = 10 ÷ 2 Pressure = 5 Pa or N/m2
  • Question 4

Type two words in the spaces to complete the sentence below.

CORRECT ANSWER
EDDIE SAYS
Remember that we need to look at our formulae pyramid and cover up the variable we are seeking. If we cover Force, then we are left with: Force = Pressure × Area As with any multiplication sum, we can mix the order of these elements if we choose, so calculating 'Pressure × Area' and 'Area × Pressure' will give the same answer.
  • Question 5

A 2 m2 object has a pressure applied to it of 7 Pa.

 

What is the force being exerted on this object?

CORRECT ANSWER
14 N
EDDIE SAYS
It's all about identifying the correct formula to use in these cases. We are looking for force so if we cover this in our pyramid, we are left with the formula: Force = Pressure × Area Now we just need to substitute our values into this formula: Force = 7 × 2 Force = 14 N
  • Question 6

Find the force acting on a 3 m2 object with a pressure of 9 Pa being applied. 

 

Type your answer as a number without a unit in the box below, as this has already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
We are seeking force again here, so we need to use the same formula as the previous question: Force = Pressure × Area Now we just need to substitute our values into this formula: Force = 9 × 3 Force = 27 N
  • Question 7

Type two words in the spaces to complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
Remember that we need to look at our formulae pyramid and cover up the variable we are seeking. If we cover Area, then we are left with: Area = Force ÷ Pressure As with any division sum, it is essential to get these two elements the right way round or we will not reach the correct answer.
  • Question 8

A force of 3 N produces a pressure of 3 Pa.

 

What is the area being affected by this pressure and force?

CORRECT ANSWER
1 m2
EDDIE SAYS
It's all about identifying the correct formula to use in these cases. We are looking for area so if we cover this in our pyramid, we are left with the formula: Area = Force ÷ Pressure Now we just need to substitute our values into this formula: Area = 3 ÷ 3 Area = 1 m2 Did you remember that, unless specified otherwise, we should express areas using the unit m2?
  • Question 9

A pressure of 4 Pa is produced by a force of 10 N.

 

What area does this force act over? 

 

Type your answer as a number without a unit in the box below, as this has already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
We are seeking area again here, so we need to use the same formula as the previous question: Area = Pressure ÷ Force Now we just need to substitute our values into this formula: Area = 10 ÷ 4 Area = 2.5 m2
  • Question 10

Match each force and volume on the left with its corresponding pressure on the right. 

CORRECT ANSWER

Column A

Column B

F = 15 N , A = 3 m2
P = 5 Pa
F = 15 N , A = 0.5 m2
P = 30 Pa
F = 2 N , A = 4 m2
P = 0.5 Pa
F = 1 N , A = 0.1 m2
P = 10 Pa
EDDIE SAYS
All of these calculations are seeking pressure so we need to apply the same formula in each case: Pressure = Force ÷ Area Pressure = 15 ÷ 3 = 5 Pa Pressure = 15 ÷ 0.5 = 30 Pa Pressure = 2 ÷ 4 = 0.5 Pa Pressure = 1 ÷ 0.1 = 10 Pa The tricky calculations here are to divide by 0.5 and 0.1. Remember that dividing by 0.5 is exactly the same as multiply by 2, whilst dividing by 0.1 is the same as multiplying by 10. You can now use the Force, Pressure, Area formulae pyramid to identify the formula to use to find a missing variable, and then apply this.
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Start your £1 trial today.
Subscribe from £10/month.