Question

Cloth having an area of 165 metre square is shaped into the form of a conical tent of radius 5 metre find the volume of the cone

Answer 1

#BAL

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