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# A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm2. Find the volume of the cone. - CBSE Class 10 - Mathematics

ConceptSurface Area of a Combination of Solids

#### Question

A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm2. Find the volume of the cone. (use π 3.14).

#### Solution

Given:
Radius of the cone, r = 3 cm

CSA of the cone = 47.1 cm2

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+h2

h2=16

h=4 cm

Volume of the cone = 1/3pir^2h

=1/3×3.14×32×4

=37.68 cm3

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Solution A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm2. Find the volume of the cone. Concept: Surface Area of a Combination of Solids.
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