Q14 of 79 Page 244

A right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled in cones of height 12 cm and diameter 6 cm, having a hemispherical shape on top. Find the number of such cones which can be filled with the ice cream available.

Given, Diameter of right circular cylinder = 12 cm


Radius of right circular cylinder (r1) =


= 6 cm


Height of right circular cylinder (h1) = 15 cm


Volume of Cylindrical ice-cream container = r12h1


= 6 6 15


= cm3


Diameter of cone = 6 cm


Radius of cone (r2) =


= 3 cm


Height of cone (h2) = 12 cm


Radius of hemisphere = radius of cone = 3 cm


⇒ Volume of cone full of ice-cream = volume of cone + volume of hemisphere


= r22h2 + r23


= ( r22h2 + 2r23)


= (32× 12 + 2× 33)


= (9 ×12 + 2 × 27)


= (108 +54)


= 162


= cm3


Let n be the number of cones full of ice cream.


⇒ Volume of Cylindrical ice-cream container = nVolume of one cone full with ice cream


= n


⇒ N =


⇒ n = 10


Hence, the required number of cones = 10


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