# Useful Formulae

## Useful Formulae Revision

**Useful Formulae**

This page contains **useful formulae** you may need in your exams. You should already be familiar with these equations from GCSE maths.

**Area Calculations**

Area is the amount of space that a 2D shape takes up.

**Squares and Rectangles**

A=xy

- x= length
- y= height

**Triangles**

A=\dfrac{1}{2}bh

- b= base
- h= height

**Parallelograms**

A=bh

- b= base
- h= perpendicular height

**Trapezia**

A=\dfrac{1}{2}(a+b)h

- a= width of the short side
- b= width of the long side
- h= height

**Circles**

You should know what the following words mean when talking about circles:

**Radius**– the distance between the entre of the circle and any point on the edge of the circle.**Diameter**– the distance between two opposite edges of the circles, passing through the centre.**Circumference**– the distance around the edge of the circle.

**Area of a Circle**

A=\pi r^2

- r= radius

**Circumference**

C=2 \pi r = \pi d

- r= radius
- d= diameter =2r

**Volume Calculations**

Volume is the amount of space a 3D shape takes up.

**Cuboid**

V=xyz

- x= width
- y= height
- z= length

**Cylinders**

V=\pi r^2 l

- r= radius
- l= length

**Triangular Prism**

V=\dfrac{1}{2}bhl

- b= base
- h= height
- l= length

**Sphere**

V=\dfrac{4}{3} \pi r^3

- r= radius

**Example 1: Calculating the Area of an Inhibition Zone. **

A biologist is performing an experiment on a new antibiotic drug. They measure a circular inhibition zone and find the diameter is 3.6 \text{ mm}.

Calculate the area of this inhibition zone.

**[3 marks]**

r=\dfrac{d}{2} = \dfrac{\textcolor{1c63ba}{3.6 \text{ mm}}}{2} = \textcolor{aa57ff}{\bold{1.8} \textbf{ mm}} \\ \bold{A=\pi r^2} = \pi \times (\textcolor{aa57ff}{1.8})^2 = \bold{10.2} \textbf{ mm}^2

**Example 2: Calculating the Volume of Water Displaced**

A wooden block with dimensions \textcolor{f95d27}{10 \text{ cm}} \times \textcolor{f43364}{6 \text{ cm}} \times \textcolor{10a6f3}{3.5 \text{ cm}} is dropped into a container of water. Calculate the volume of water displaced by the wooden block.

**[2 marks]**

## Useful Formulae Example Questions

**Question 1: **Calculate the area of a square with sides of length 6 \text{ cm}.

**[2 marks]**

**Question 2: **Calculate the volume of a sphere with radius 40 \text{ mm}.

**[2 marks]**

**Question 3: **Calculate the circumference of a circle with a diameter of 2 \text{ m}.

**[2 marks]**

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