Q. 135.0( 2 Votes )

# If the slant height of a cone is 18.7 cm and the curved surface area is 602.8 cm^{2}, find the volume of cone. (π = 3.14)

Answer :

Given.

Slant height of cone = 18.7 cm

CSA of cone = 602.8 cm^{2}

Formula used/Theory.

Volume of cone = πr^{2}h

CSA of cone = πrl

In cone,

CSA of cone = 602.8 cm^{2}

πrl = 602.8 cm^{2}

3.14 × r × 18.7cm = 602.8 cm^{2}

r = = 10.26 cm

In cone,

The Radius, height and slant height makes a right angled triangle

With hypotenuse as slant height of triangle

∴ By Pythagoras Theorem

Radius^{2} + Height^{2} = (slant height) ^{2}

Height^{2} + (10.26 cm) ^{2} = (18.7 cm) ^{2}

Height^{2} + 105.26 cm^{2} = 349.69 cm^{2}

Height^{2} = 349.69 cm^{2} – 105.26 cm^{2}

Height = √(244.43 cm^{2}) = 15.63 cm

Volume of Cone = πr^{2}h

= × 3.14 × 10.26cm × 10.26cm × 15.63cm

= 3.14 × 10.26cm × 10.26cm × 5.21cm

= 1722.11 cm^{3}

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