A cloth having an area of 165\; m^{2} is shaped into the form of a conical tent of radius 5\; m

  1. How many students can sit in the tent if a student, on an average, occupies \frac{5}{7}m^{2} on the ground?
  2. Find the volume of the cone.

 

Answers (1)

Answer : (i) 110 students

                (ii) 241.73\; m^{3}

We have, Area of cloth =165\; m^{2}

This cloth is shaped in the form of a conical tent.

Radius of conical tent = 5 cm

So, we have:

Area of cloth = Curved surface area of cone 

Curved surface area of cone is given as \pi rl   Where, r = radius of a cone

                                                                                l = slant height of a cone

So curved surface area of conical tent,

165=\frac{22}{7}\times 5 \times l

\Rightarrow l=\frac{165 \times 7}{22 \times 5}=\frac{21}{2}=10.5\; m

(i) Now it is given that area covered by 1 student =\frac{5}{7}m^{2}

\text {So the number of students}=\frac{\text {Area of a circular base of a cone}}{\text {Area covered by 1 student}}

\Rightarrow \text {Number of student}=\frac{\pi r^{2}}{\frac{5}{7}}=\frac{\left ( \frac{22}{7}\times 5^{2} \right )}{\frac{5}{7}}=110

So 110 students can sit in the tent.

(ii) Volume of cone : \frac{1}{3}\pi r^{2}h

For a right circular cone, we have

r^{2}+h^{2}=l^{2}

\Rightarrow 5^{2}+h^{2}=\left ( 10.5 \right )^{2}

\Rightarrow 25+h^{2}=110.25

\Rightarrow h^{2}=110.25-25=85.25

h=\sqrt{85.25}=9.23\; m

So, volume =\frac{1}{3}\times \frac{22}{7}\times 5^{2}\times 9.23

=\frac{5076.5}{21}=241.73\; m^{3}

 

 

 

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