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

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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. (use π 3.14).

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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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2015-2016 (March) Delhi Set 2

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