A container which is cylindrical in shape having diameter 16 cm and height 40 cm is full of ice cream ice cream to be filled into cones of height 12 cm and diameter 4 cm having a hemispherical shape on top find the number of such coins which can be filled with ice cream
Answers
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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Hope this will help you.... bebrainly