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How do I find the volume of a square pyramid? Diagonal length is 4cm and the height is 3cm

[Grade 9 Math]

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1 Answer

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The volume of a pyramid is given by $$V=\frac{lwh}3$$ where $l$ and $w$ are the lengths of the sides of the base and $h$ is the height

We know that our base is square, so $l=w$ and we can therefore see the following

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We can use Pythagoras' theorem to find $w$:

\begin{align}w^2+w^2&=4^2\\ 2w^2&=16\\ w^2&=8\\ w&=\sqrt8\\ &=2\sqrt 2\end{align}

Now we can use the formula from above to find the volume:

\begin{align}V&=\frac{lwh}3\\ &=\frac{w^2h}3\\ &=\frac{(2\sqrt 2)^2\times 3}3\\ &=\frac{8\times3}3\\ &=8\text{ cm}^3\end{align}

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