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A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm^{2}. Find the volume of the cone. (use π 3.14).

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#### Solution

Given:

Radius of the cone, *r* = 3 cm

CSA of the cone = 47.1 cm^{2}

Let *h* and *l* be the height and slant height of the cone, respectively.

CSA of the cone = 47.1 cm2

πrl=47.1

⇒3.14×3×l=47.1

`=>l = 47.1/9.42`

⇒l=5 cm

`l = sqrt(r^2+h^2)`

`=>5=sqrt(3^2+h^2)`

⇒25=9+h^{2}

⇒h^{2}=16

⇒h=4 cm

Volume of the cone = `1/3pir^2h`

=`1/3`×3.14×3^{2}×4

=37.68 cm^{3}

Concept: Surface Area of a Combination of Solids

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