Question

31.16 ftWhat is the volume of the pyramid?17 ft16 ft

Answer 1

Given: A pyramid with the following dimensions

`\begin{gathered} base-length(l)=16cm \\ base-width(w)=16cm \\ slant-height(h)=17cm \end{gathered}`

To Determine: The volume of the given pyramid

Solution

The volume of a pyramid is given by the formula below

`Volume(Pyramid)=(1)/(3)* base-area* height(pyramid)`

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

`\begin{gathered} b=(1)/(2)* l \\ b=(1)/(2)*16cm \\ b=8cm \\ So, \\ H^2+8^2=17^2 \\ H^2=17^2-8^2 \\ H^2=289-64 \\ H^2=225 \\ H=√(225) \\ H=15cm \end{gathered}`

Therefore, the volume of the pyramid would be

`\begin{gathered} Volume(Pyramid)=(1)/(3)*16cm*16cm*15cm \\ Volume(Pyramid)=16cm*16cm*5cm \\ Volume(Pyramid)=1280cm^3 \end{gathered}`

Hence, the volume of the given pyramid is 1280cm³