Question

URGENT!!!!!
Find the volume of the composite solid shown. The radius of the cylinder is 2m.

Answer 1

400.3 m³ (nearest tenth)

Explanation:

The composite solid comprises:

• A cylinder with height of 4 m and radius of 2 m.
• A rectangular prism with dimensions 10 m x 5 m x 7 m.

`\boxed{\begin{minipage}{3.4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}`

Therefore, the volume of the cylinder is:

`\begin{aligned}\implies V_(\sf cyclinder)&=\pi \cdot 2^2 \cdot 4\\&=\pi \cdot 4 \cdot 4\\&=16 \pi \; \sf m^3\end{aligned}`

`\boxed{\begin{minipage}{5 cm}\underline{Volume of a rectangular prism}\\\\$V=w\:l\:h$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width of the base. \\ \phantom{ww}$\bullet$ $l$ is the length of the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}`

Therefore, the volume of the rectangular prism is:

`\begin{aligned}\implies V_(\sf rectangular\;prism)&=7 \cdot 10 \cdot 5\\&=70 \cdot 5\\&=350 \; \sf m^3\end{aligned}`

Therefore the volume of the composite solid is:

`\begin{aligned}\implies V_(\sf composite\;solid)&=V_(\sf cycinder)+V_(\sf rectangular\;prism)\\&=16 \pi +350\\&=400.2654825\\&=400.3\; \sf m^3\;\;(nearest\;tenth)\end{aligned}`