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Question

A container shaped like a right circular cylinder has a diameter (d) equal to 12 cm and height (h) equal to 15 cm is full of ice cream. The ice cream is to be filled into 10 equal cons having a hemispherical shape on the top. If the height of the cone is 4 times its radius, find the height of the cone.


Solution

Given:

For right circular cylinder

Diameter = 12 cm

Radius(R1) = 12/2= 6 cm & height (h1) = 15 cm

Volume of Cylindrical ice-cream container= πr1²h1= 22/7 × 6× 6× 15= 11880/7 cm³

Volume of Cylindrical ice-cream container=11880/7 cm³
For cone, 

Diameter = 6 cm

Radius(r2) =6/2 = 3 cm & height (h2) = 12 cm
Radius of hemisphere = radius of cone= 3 cm

Volume of cone full of ice-cream= volume of cone + volume of hemisphere

= ⅓ πr2²h2 + ⅔ πr2³= ⅓ π ( r2²h2 + 2r2³)

= ⅓ × 22/7 (3²× 12 + 2× 3³)

= ⅓ × 22/7 ( 9 ×12 + 2 × 27)
= 22/21 ( 108 +54)

= 22/21(162)

= (22×54)/7

= 1188/7 cm³


Let n be the number of cones full of ice cream.


Volume of Cylindrical ice-cream container =n × Volume of one cone full with ice cream.
11880/7 = n × 1188/7

11880 = n × 1188

n = 11880/1188= 10

n = 10

Hence, the required Number of cones = 10

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