Question

5. A container shaped like a right circular cylinder having diameter 12 cm. and height 15 cm.
is full of ice cream. The icecream 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.​

Answer 1

SOL :-

⇒  Number of cones = Volume of cylinder    

                                     Volume of ice-cream cone

⇒Volume of cylinder

$\red{Diameter}$ = 12cm

$\yellow{Radius}$ =  Diameter       = 6cm

                                                     2

$\blue{Height}$ = 15cm

Volume of cylinder = πr^2h

                                = π(6)^2*(15)

                               =540π

Volume of ice cream = Volume of cone + Volume of Hemisphere

VOLUME OF CONE

$\red{Diameter}$ = 6cm

$\yellow{Radius}$ =  Diameter       = 3cm

                                                     2

$\blue{Height}$ = 12cm

Volume of ice cream cone = 1  πr^2h

                                                 3

                                   =  1   * π*(3)^2*(12)

                                       3

                                =36π

VOLUME OF HEMISPHERE

$\yellow{Radius}$ =  Diameter       = 3cm

                                                     2

VOLUME OF HEMISPHERE =  2 πr^3

                                                     3

                                         = 18π

hence,

⇒Volume of ice cream cone = volume of cone+ volue of hemisphere

⇒36π + 18π

⇒54π

Now,

number of cones = Volume of cylinder

                                Volume of ice cream cone

                   =540π

                     54π

               =10

SO, THE NUMBER OF CONES IS 10