Question

A cloth having an area of$165m^2$ is shaped into the form of a conical tent of radius $5m$ , How many students can sit in the tent if a student, on an average, occupies$\frac{5}{7}{m}^2$ on the ground?

Answer 1

According to the question,

Area of cloth $=165m^2$

The radius of conical tent$=5m$

Area covered by $1$student $=\frac{5}{7}{m}^2$

The curved surface area of cone $=\pi rl$

Thus, the curved surface area of a conical; tent $=\pi rl$

$$\begin{gathered} \Rightarrow 165=\frac{22}{7}\times 5\times l \\ \Rightarrow l=\frac{165\times 7}{22\times 5}=\frac{21}{2}=10.5m \end{gathered}$$

Number of students $=\frac{Areaofthebase}{Areaoccupiedbyonestudent}$

Number of students$=\frac{\pi r^2}{{\displaystyle \frac{5}{7}}}=\frac{{\displaystyle \frac{22}{7}}\times 5^2}{{\displaystyle \frac{5}{7}}}=22\times 5=110$

Hence, number of students who can sit in the tent are $110$.