A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
10
Let number of cones which can be filled = n
Diameter of cylinder = d = 12 cm
⇒ Radius of cylinder =
r=d2=122=6 cm
Height of cylinder = h = 15 cm
Volume of cylinder = π.r2.h=(π×62×15)=540π cm3
Diameter of cone = d1=6 cm
Radius of cone = r1=d12=62=3 cm
Height of cone = h1=12 cm
Volume of cone =13π(r1)2h1=13×π×32×12=36π cm3
Radius of hemispherical top of the cone = r1=3 cm
Volume of hemisphere top =23π(r1)3=23×π×33=18π cm3
According to given condition we have:
n × ( Volume of Cone + Volume of Hemispherical top ) = volume of cylinder
⇒ n × (36 π+18π)=540π
⇒ n × (54 π)=540π
n=54054=10