. 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 in 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-crcam.
Answers
Step-by-step explanation:
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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