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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).
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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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