top of page
Circumference, Area,
Surface Area, and Volume
By Taylor Winter
Derive the Formula:
Volume of a Pyramid/Cone
Example Problems
1. A square pyramid has a base side length of 3 cm and a height of 6 cm. What is the volume?
​
Volume of a pyramid= 1/3(B x h)
B= 3 cm x 3 cm= 9 cm^2 h= 6 cm
​
1/3(9cm^2 x 6 cm)= 1/3(54 cm^3)= 18cm^3
​
The volume of the pyramid is 18 cm^3.
The volume of a prism/cylinder is the area of the base x the height of the shape.
​
Area of the base is represented as capitol B where as base is represented as lower case b.
​
The volume of a pyramid/cone is equal to 1/3 of a prism/cylinder of the same height and base.
​
Therefore the formula is 1/3(B x h).
2. A cone has a radius of 6 cm and a height of 10 cm. What is the volume?
​
Volume of a cone= 1/3(B x h)
B= πr^2= 36πcm^2 h= 10 cm
​
1/3(36πcm^2 x 10 cm)= 1/3(360πcm^3)= 120πcm^3
​
The volume of the pyramid is 120πcm^3.
bottom of page