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 into 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 cream.
Answers
Answer:
The required number of cones which can be filled with ice-cream is 10
Step-by-step explanation:
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
Volume of cone full of ice-cream = 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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Step-by-step explanation:
Answer is in Attachment
