Q11 of 48 Page 264

The height and the slant height of a cone are 12 cm and 20 cm respectively. Find its volume. (π = 3.14)

Given.


Slant height of cone = 20 cm


Height of cone = 12 cm


Formula used/Theory.


Volume of cone = πr2h


In cone,


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


With hypotenuse as slant height of triangle


∴ By Pythagoras Theorem


Radius2 + Height2 = (slant height) 2


Radius2 + (12 cm) 2 = (20 cm) 2


Radius2 + 144 cm2 = 400 cm2


Radius2 = 400 cm2 – 144 cm2


Radius = √(256 cm2) = 16 cm


Volume of Cone = πr2h


= × 3.14 × 16cm × 16cm × 12cm


= 3.14 × 16cm × 16cm × 4cm


= 3215.36 cm3


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