Question

Find the volume of the shaded solid. Round your answer to 2 decimal places if necessary. Use 3.14 when necessary.

Answer 1

Given the figure below:

To find the volume of the shaded solid, we subtract the volume of the cylinder from the volume of the entire cuboid.

step 1: Evaluate the volume of the cuboid.

The volume of the cuboid is expressed as

`\begin{gathered} Volume=length* width* height \\ thus,\text{ we have} \\ V_(cuboid)=24*6*6 \\ =864\text{ }m^3 \end{gathered}`

step 2: Evaluate the volume of the cylinder.

The volume of a cylinder is expressed as

`\begin{gathered} Volume=\pi*(radius)^2* height \\ thus,\text{ we have} \\ V_(cylinder)=3.14*((6)/(2))^2*24 \\ =678.24\text{ }m^3 \end{gathered}`

step 3: Evaluate the volume of the shaded solid.

Thus, we have

`\begin{gathered} V_{shaded\text{ solid}}=V_(cylinder)-V_(cuboid) \\ =864-678.24 \\ =185.76 \end{gathered}`

Hence, to 2 decimal places, the volume of the solid figure is evaluated to be

`185.76\text{ m}^3`