a container shaped like a right circular cylindar having diameter 6cm and height 7.5cm is full of ice cream. The ice cream is to be filled into cones of height 6cm and diameter 3cm, having a hemispherical shape on the top. Find the number of cones which can be filled with ice cream

Step-by-step explanation:

Cylinder:

d = 6cm; r = 6/2 = 3cm

h = 7.5cm

Volume of ice cream in cylinder = πr²h

= π * 3 * 3 * 7.5 = 67.5 π cubic cm

Cone:

h = 6 cm;

d = 3cm; r = 3/2 = 1.5cm

Volume = (1/3) πr²h

= (1/3) * π * 1.5 * 1.5 * 6

= π * 1.5*1.5 * 2 = 4.5π cu. cm

Hemisphere on top:

r = 1.5cm

Volume = (2/3) πr³

= (2/3) * π * 1.5 * 1.5 * 1.5

= 2 * π * 0.5*1.5*1.5

= 2.25π cu. cm

Volume of ice cream in each cone = 4.5 π + 2.25π = 6.75π cubic cm

No of cones = volume of cylinder / Volume of ice cream in each cone

=π * 67.5 / 6.75 * π

= 67.5 * 100 / 6.75 * 100

= 6750 / 675

= 10

number of cones which can be filled with ice cream = 10 cones