Given: A pyramid with the following dimensions
[tex]\begin{gathered} base-length(l)=16cm \\ base-width(w)=16cm \\ slant-height(h)=17cm \end{gathered}[/tex]
To Determine: The volume of the given pyramid
Solution
The volume of a pyramid is given by the formula below
[tex]Volume(Pyramid)=\frac{1}{3}\times base-area\times height(pyramid)[/tex]
Let us determine the height of the pyramid
From the above, H is the height of the pyramid, and b is the half of the base length. We can determine H, using the Pythagoras theorem
[tex]\begin{gathered} b=\frac{1}{2}\times l \\ b=\frac{1}{2}\times16cm \\ b=8cm \\ So, \\ H^2+8^2=17^2 \\ H^2=17^2-8^2 \\ H^2=289-64 \\ H^2=225 \\ H=\sqrt{225} \\ H=15cm \end{gathered}[/tex]
Therefore, the volume of the pyramid would be
[tex]\begin{gathered} Volume(Pyramid)=\frac{1}{3}\times16cm\times16cm\times15cm \\ Volume(Pyramid)=16cm\times16cm\times5cm \\ Volume(Pyramid)=1280cm^3 \end{gathered}[/tex]
Hence, the volume of the given pyramid is 1280cm³
