Question

Find the volume of each pyramid. Round your answer to the nearest tenth, if necessary. Do not include units (i.e. in, ft, cm, etc.). (FR)

Answer 1

The volume of a pentagonal pyramid is given below as

`V=(1)/(3)* area\text{ of base}*\text{ height}`

Step 1:

The base is a pentagon which contains 5 regular triangles of same base

`\begin{gathered} base=8cm \\ h=5.5cm \end{gathered}`

Area of a triangle is

`\begin{gathered} A_(triangle)=\frac{1}{2\text{ }}* base\text{ }* height \\ A_(triangle)=(1)/(2)*8cm*5.5cm \\ A_(triangle)=22cm^2 \end{gathered}`

Then the area of the base will be

`\begin{gathered} A_(base)=5* area\text{ of each triangle} \\ A_(base)=5*22cm^2 \\ A_(base)=110cm^2 \end{gathered}`

Therefore,

The volume of the pyramid will be

`\begin{gathered} V_(pyramid)=(1)/(3)* basearea* height \\ V_(pyramid)=(1)/(3)*110cm^2*12cm \\ V_(pyramid)=440cm^3 \end{gathered}`

Hence,

The final answer is

`\Rightarrow440`