# Useful Formulae

GCSEAQAFoundationHigher

## 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
GCSEAQA

## 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 $=2r$
GCSEAQA

## 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
GCSEAQA

## 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]

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

GCSEFoundationHigherAQA

## 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]

\text{volume of water displaced} \\ \begin{aligned} &= \text{volume of the block} \\ &= xyz \\ &= \textcolor{f95d27}{10} \times \textcolor{f43364}{6} \times \textcolor{10a6f3}{3.5} \\ &= \bold{210} \textbf{ cm}\bold{^3} \end{aligned}

GCSEAQA

## Useful Formulae Example Questions

\begin{aligned} \bold{A} &= \bold{xy} \\ &= 6 \times 6 \\ &= \bold{36} \textbf{ cm}\bold{^2} \end{aligned}

Gold Standard Education

\begin{aligned} \bold{V} &= \bold{\dfrac{4}{3} \pi r^3} \\ &= \dfrac{4}{3} \times \pi \times 40^3 \\ &= \bold{268 \, 083} \textbf{ mm}\bold{^3} \end{aligned}

\begin{aligned} \bold{C} &= \bold{\pi d} \\ &= \pi \times 2 \\ &= \bold{6.28} \textbf{ m} \end{aligned}