043. What is the volume of a cylindrical container of base diameter 49 cm and height 40 cm? (A) 75460 cu.cm (B) 52460 cu.cm (C) 42360 cu.cm (D (D) 36360 cu.com
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A cylindrical container of radius 6 cm and height 15 cm is fulled with ice-cream. The whole ice-cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice-cream cone
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Correct option is
A
3 cm
Given, Radius of cylindrical container =6cm
Height of cylindrical container =15cm
Volume of cylinder =πr
2
h
=π×36×15
=540πcm
3
Now, as it has to be divided among 10 children
∴ Dividing volume by 10=
10
540
=54πcm
3
Volume of cone + Volume of hemispherical top = Volume of ice-cream in it.
⇒
3
1
πr
2
h+
3
2
πr
3
=πr
2
h
⇒
3
1
πr
2
(4r)+
3
2
πr
3
=54π
⇒
3
1
πr
3
(4+2)=54π
⇒2r
3
=54⇒r=3
Hence, the radius of icecream cone =3 cm.
solution