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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

User Cmcromance
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1 Answer

2 votes

Answer:

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

User HaoZeke
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