Question

Find the volume of the garden shed

Answer 1

47.3 m³

Explanation:

The garden shed is made up of a rectangular prism and a pyramid.

Volume of a rectangular prism

`\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width * length * height\\&=4 * 4 * 2\\&=16 * 2\\&=32\;\; \sf m^3\end{aligned}`

Volume of a pyramid

From inspection of the given diagram, the slant height of the pyramid is 3.5 m.

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

`\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=√(8.25)\;\; \sf m\end{aligned}`

Therefore:

`\begin{aligned}\textsf{Volume of a pyramid}&=(\sf length * width * height)/(3)\\\\&=(\sf 4 * 4 * √(8.25))/(3)\\\\& = 15.31883372\;\; \sf m^3\end{aligned}`

Volume of the garden shed

`\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}`