Volume of a pyramid
The volume of a pyramid is \(\frac{1}{3}\) of the volume of a prism with the same base and height.
The volume of a pyramid can be calculated using the formula:
\(\text{volume of a pyramid} = \frac{1}{3} \times \text{area of base} \times \text{perpendicular height}\)
The perpendicular height, (h), is the height of the pyramid measured at a right angle from the base.
Question
Find the volume of this square-based pyramid:
The volume is \(= \frac{1}{3} \times \text{b} \times \text{h}\)
First find \(h\). You can use Pythagoras theorem to do this.
\(h^2=\text{hypotenuse}^2-\text{side}^2\)
\(h^2=6^2 - {\frac{5}{2}}^2\)
\(h^2=29.75\)
\(h=5.45\)
Now you can work out the volume
\(\text{volume}= \frac{1}{3} \times 5 \times 5 \times 5.45\)
\(\text{volume}= \frac{1}{3} \times 5 \times 5 \times 5.45\)
\(= \frac{1}{3} \times 136.25\)
\(= 45.42cm^3\)
More guides on this topic
- Determine the gradient of a straight line
- Circle geometry
- Applying Pythagoras Theorem
- Applying the properties of shapes to determine an angle
- Using similarity
- Working with two-dimensional vectors
- Working with three-dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector
- An Approximate History of Co-ordinates