Question

52. From a circular canvas of radius 28 m, a sector of
270° was cut out and a conical tent was formed by
joining the straight ends of this piece. The volume
of the tent is
(1) 298212 m3
(2) 27247 m
(4) 1734,2 m3
(3) 323477 m3​

Answer 1

Let r be the base radius of the cone.

Angle of the sector, θ=120o

Radius of the sector, R=21cm

When the sector is folded into a right circular cone, we have circumference of the base of the cone= Length of the arc

⇒2πr=360oθ×2πR

⇒r=360oθ×R

Thus, the base radius of the cone, r=360o120o×21=7cm

Also, the slant height of the cone,

l= Radius of the sector

Thus, l=R ⇒ l=21cm

Now, the curved surface area of the cone,

CSA=πrl

=722×21=462

Thus, the curved surface area of the cone is 462sq.cm