A right circular cone of radius 3 ππ, has a curved surface area ofΒ 47.1cm2Find the volume of the cone. (Use Ο = 3. 14)Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  (OR)In the given figure, βπππ is an equilateral triangle of side 8 ππ and π·, πΈ, πΉ are centres of circular arcs, each radius 4 ππ. Find the area of shaded region. (Use Ο = 3. 14 andΒ Β 3Β Β Β Β  = 1. 732)Β

# A right circular cone of radius 3 ππ, has a curved surface area of 47.1cm2Find the volume of the cone. (Use Ο = 3. 14)                                                (OR)In the given figure, βπππ is an equilateral triangle of side 8 ππ and π·, πΈ, πΉ are centres of circular arcs, each radius 4 ππ. Find the area of shaded region. (Use Ο = 3. 14 and  $\sqrt{3}$     = 1. 732)

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### Solution:

We need to find the volume of the cone of radius 3 ππ provided that its curved surface area of 47.1 cm2.
It is known that the CSA of a cone is given as πΆππ΄ = Οππ, where π and π are the radius and slant height respectively.
On substituting the values, we get the slant height as
β 47. 1 = Ο(3)π
β 47. 1 = 9. 42π
β π = 5 ππ
Now, the height of the cone can be given as
β = $\sqrt{{5}^{2}-{3}^{2}}$
β β = $\sqrt{16}$
β β = 4 ππ
Also, the volume of the cone is given by π = 1/3Οπ2 h . On substituting the values, we get
3 Οπ β
β π = 1/3 Ο x 3 x 4
β π = 37.68 cm3
Hence, the volume of the cone is 37.68 cm3

(OR)

We need to find the area of shaded region provided that βπππ is an equilateral triangle of side 8 ππ and π·, πΈ, πΉ are centres of circular arcs, each radius 4 ππ.

It can be observed that the arcs form the sector in the triangle and hence, the area of shaded region is

π΄πππ ππ π βππππ ππππππ = π΄πππ ππ βπππ β 3(π΄πππ ππ π πππ‘ππ)

β π΄πππ ππ π βππππ ππππππ =

β π΄πππ ππ π βππππ ππππππ =

Hence, the area of the shaded region is  2.592 cm2.

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