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Solution


Q.

Assertion (A): From a solid cylinder whose height is 12 cm and diameter is 10 cm, a conical cavity of same height and same diameter is hollowed out. Volume of the cone is 22007cm³.

Reason (R): If a conical cavity of same height and same diameter is hollowed out from a cylinder of height h and base radius r, then volume of the cone is equal to 1/2 of the volume of the cylinder.
1 Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).  
2 Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for Assertion (A).  
3 Assertion (A) is true but Reason (R) is false.  
4 Assertion (A) is false but Reason (R) is true.  

Ans.

(3)

Radius of cone, r=102cm=5cm

Height of cone, h=12cm

Volume of cone=π3r2h

=13×227×5×5×12

=110×6021=660021=22007 cm3So, Assertion (A) is true.

Also volume of cylinder=πr2h and

conicalcavity=13πr2h

⇒13(volume of cylinder)=volume of cone.

Hence, Assertion (A) is true but Reason (R) is false.