Question

6. A cloth having an area of 165 2 is shaped into the form of a conical tent of radius 5 cm.
I) How many students can sit in the tent if a student on an average, occupies 57 2 on the ground?
ii) Find the volume of the cone.

Answer 1

Let l m be the height of the conical tent.

Radius of the base of conical tent (r) = 5 m

(i) Area of the circular base of the cone = πr2 = 22/7 x 52 m2

Number of students = Area of the base/Area occupied by one student

= 22/7 x 5 x 5 m2/ 5/7 m2

= 22/7 x 5 x 5 x 7/5 = 110

(ii) Also, curved surface area of cone = πrl

⇒ 165 = 22/7 x 5 x l

⇒ l = 165 x 7/22 x 5 ⇒ l = 21/2 m = 10.5 m

Also, h2 = l2 - r2

⇒ h = root under(√(10.5)2 - 52) = root under(√15.5 x 5.5)

= root under(√85.25) ~ 9.23 cm

Volume of conical tent = 1/3πr2h

= 1/3 x 22/7 x 52 x 9.23 m3 = 241.74 m3

Answer 2

Answer:

I) 110

II) 241.74m^3

Step-by-step explanation:

Let l m be the height of the conical tent.  

Radius of the base of conical tent (r) = 5 m

(i) Area of the circular base of the cone = πr2 = 22/7 x 52 m2

Number of students = Area of the base/Area occupied by one student  

= 22/7 x 5 x 5 m2/ 5/7 m2

= 22/7 x 5 x 5 x 7/5 = 110

(ii) Also, curved surface area of cone = πrl  

⇒ 165 = 22/7 x 5 x l

⇒  l = 165 x 7/22 x 5  ⇒ l = 21/2 m = 10.5 m

Also,  h2 = l2 - r2

⇒  h = root under(√(10.5)2 - 52) = root under(√15.5 x 5.5)

= root under(√85.25) ~ 9.23 cm

Volume of conical tent = 1/3πr2h

= 1/3 x 22/7 x 52 x 9.23 m3 = 241.74 m3

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