A container shaped like a right circular cylinder having diameter 12cm and height 15cm is full of ice cream.the ice cream is to be filled into cones of height 12cm and diameter 6cm having hemispherical top.Find number of cones which can be filled with ice cream.
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Let height of cone right circular cone be,h=15cm. (Given)
diameter,d=12cm
radius,r=6cm
Let Height of ice cream cone be,H=12cm
Diameter,D=6 cm
Radius,R=3cm. Let no.of cones be n
Vol.of right circular cone= vol.of right circular cone×n
1/3π*r2h=1/3π*2RH
diameter,d=12cm
radius,r=6cm
Let Height of ice cream cone be,H=12cm
Diameter,D=6 cm
Radius,R=3cm. Let no.of cones be n
Vol.of right circular cone= vol.of right circular cone×n
1/3π*r2h=1/3π*2RH
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Volume of the container=πr²h cu.units
=π(12/2)²×15 cm³=π×6²×15=540π cm³
Volume of cone=1/3×π(6/2)²×12 cm³=1/3×π×3²×12=36π cm³
Radius of the hemispherical top=Radius of the cone=6/2=3 cm
Volume of the hemispherical top=2/3π(3)³=18π cm³
Volume of the 1 total ice cream cone=36π+18π=54π cm³
Required No.of cones=540π/54π=10(Ans.)
=π(12/2)²×15 cm³=π×6²×15=540π cm³
Volume of cone=1/3×π(6/2)²×12 cm³=1/3×π×3²×12=36π cm³
Radius of the hemispherical top=Radius of the cone=6/2=3 cm
Volume of the hemispherical top=2/3π(3)³=18π cm³
Volume of the 1 total ice cream cone=36π+18π=54π cm³
Required No.of cones=540π/54π=10(Ans.)
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