Question

A cloth having an area of 165 m^2 is shaped into the form of a conical tent of radius 5m.
1. How many students can sit in the tent if a student,on an average, occupies 5/7 m^2 on the ground?
2. Find the volume of the cone.

Answer 1

Heya mate
The answer of ur question is in the attachment



Hope it helps

Answer 2

1. Here r, radius of cone = 5m

Area of cloth = Curved surface area of tent

=> 165 = πrl

$= > \frac{22}{7} \times 5 \times l = 165 \\ \\ l = \frac{165}{5} \times \frac{7}{22} \\ \\ l = \frac{21}{2} m \\ \\ no. \: of \: students \: who \: can \: sit \: inside \: = > \\ \\ \frac{area \: of \: base}{area \: occupied \: by \: one \: student} \\ \\ = > \frac{\pi r {}^{2} }{\frac{5}{7}} = > \frac{7\pi r {}^{2} }{5} \\ \\ = > \frac{7 \times \frac{22}{7} \times 5 \times 5}{5} \\ \\ = > 7 \times \frac{22}{7} \times 5 \\ \\ = > \: 22 \times 5 \\ \\ = > 110. \\ therefore \: 110 \: students \: can \: sit \: in \: the \: tent.$

$2. \: height \: (h) \: of \: cone \: = \sqrt{ {l}^{2} - {r}^{2} } \\ \\ \sqrt{( \frac{21}{2}) {}^{2} - {5}^{2} } \\ \\ \sqrt{ \frac{441 - 100}{4} } = \frac{ \sqrt{341} }{2} \\ \\ therefore \: volume \: of \: air \: in \: tent \: = > \frac{1}{3} \pi {r}^{2} h \\ \\ = > \frac{1}{3} \times \frac{22}{7} \times 5 \times 5 \times \frac{ \sqrt{341} }{2} \\ \\ = > \frac{1}{3} \times \frac{22}{7} \times 25 \times \frac{ \sqrt{341} }{2} \\ \\ = > \frac{1}{3} \times \frac{11}{7} \times 25 \sqrt{341} \\ \\ \frac{275 \sqrt{341} }{21} \\ \\ = > 241.73 \: m {}^{3}$