Question

Find the volume of the composite solid. Round your answer to the nearest tenth

Answer 1

Hint: Volume of composite solid = Volume of cylinder - Volume of hemisphere

Given

Height of cylinder = $11in$

Height of cone = $6ft$

Diameter of cylinder = Diameter of hemisphere =$6in$

Radius of cylinder =Radius of hemisphere = $=\frac{6}{2}=3in$

Volume of composite solid $=\mathrm{\pi }{\left(\mathrm{r}\right)}^2\mathrm{h}-\frac{2}{3}\mathrm{\pi }{\left(\mathrm{r}\right)}^3$

Volume of composite solid

$$\begin{gathered} =\mathrm{\pi }{\left(3\right)}^{2}11-\frac{2}{3}\mathrm{\pi }{\left(3\right)}^3=99\mathrm{\pi }-18\mathrm{\pi } \\ =81\mathrm{\pi } \\ =254.46 \end{gathered}$$

Final Answer: Volume of composite solid is about $254.5i{n}^3$