Question

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

Answer 1

Hint: Volume of composite solid = Volume of rectangular prism + Volume of hemisphere

Step 1: Given

Length of rectangular prism = Width of rectangular prism = Height of rectangular prism = $8$ cm

Diameter of hemispherical prism = Diagonal of rectangular prism $=8\sqrt{3}$

Radius of hemispherical prism = $\frac{8\sqrt{3}}{2}=4\sqrt{3}cm$

Step 2: Volume of composite solid = length * width * height $+\frac{2}{3}\mathrm{\pi }{\left(\mathrm{r}\right)}^3$

Step 3:Volume of composite solid

$$\begin{gathered} =8*8*8+\frac{2}{3}\mathrm{\pi }{\left(4\sqrt{3}\right)}^3 \\ =512+8\sqrt{3}\mathrm{\pi } \\ =555.53 \end{gathered}$$

Final Answer: Volume of composite solid is about is $555.53{\mathrm{cm}}^3$