Volume

 

What is Volume?

Volume is the measure of how much space a 3D shape occupies.
It is measured in cubic units such as $cm^3$, $m^3$, $mm^3$, etc. You need to be able to calculate the volume of:

• Cubes & Cuboids

• Prisms

• Cylinders

• Pyramids

• Cones

• Spheres

Volume of Common 3D Shapes

Cube & Cuboid:

where:

• l = length

• w = width

• h = height

 

Prism:

$$V = A \times l$$

 

 

where:

• A = area of cross-section

• l = length of the prism

 

Cylinder:

$$V = \pi r^2h$$

 

 

where:

• r = radius of the circular base

• h = height

 

Pyramid:

where:

• A = base area

• h = perpendicular height

 

Cone:

where:

• r = radius of base

• h = perpendicular height

 

Sphere:

where:

• r = radius

Example: Volume of a Pyramid

Given a square based pyramid as follows:

• Height (h) = 15 cm

• length = 6cm

• width = 6cm

 

 

 

Step 1: Use the Pyramid Formula

Step 2: Find the base area $A$

Step 3: Use Formula to find Volume

$$V = \frac{1}{3}Ah \\  \frac{1}{3} \times 36 \times 15 = 180$$

Final Answer: $180 cm^3$