(Q14).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.

nx=

Answer:

Let the number of cones that can be filled with the ice-cream be ‘n’.

Then total volume of all the cones with a hemi spherical top = Volume of the ice-cream

Ice-cream cone = Cone + Hemisphere = πr2h

n[
1
3
 πr2h +
2
3
 πr3] = πR2h

Cone:

Radius =
d
2
 =
= cm

Height, h = 12 cm

Volume V =
1
3
 πr2h
=
×
× × ×
=
×
=

Hemisphere:

Radius =
d
2
 =
= cm
Volume V =
2
3
 πr3
=
× × ×
=
×
=
∴ Volume of each cone with ice-cream =
+
=
cm3

Cylinder:

Radius =
d
2
 =
= cm

Height, h = 15 cm

Volume V = πr2h

=
× × ×
=
××
=
∴
= ×

⇒ n =
×
=

∴ n = .