Question

Find the volume of the composite solid. I have my work shown for problem 8. But somehow I’m not getting the correct answer. So, hopefully you can help me! :)

Answer 1

Given: A composite solid

To Determine: The volume of the given solids

Solution

The diameter of the cone is the same as the length of the prism. Therefore, the diameter is 4cm

`\begin{gathered} Volume-of-a-cone=(1)/(3)\pi r^2h \\ r=(d)/(2)=(4cm)/(2)=2cm^2 \end{gathered}`
`\begin{gathered} V_(cone)=(1)/(3)*\pi*2^2*4 \\ =(16)/(3)\pi cm^3 \\ =16.76cm^3 \end{gathered}`

Volume of the rectangular prism is

`\begin{gathered} V_(prism)=length* width* height \\ =4cm*4cm*4cm \\ =64cm^3 \end{gathered}`

The volume of the composite solid is

`\begin{gathered} V_(solid)=V_(prism)-V_(cone) \\ =64cm^3-16.76cm^3 \\ =47.24cm^3 \end{gathered}`

Hence, the volume of the composite solid is 47.24cm³