A cylinder with having a diameter of 21 cm & a height of 38 cm is full of ice cream. The ice cream is to be filled in cones of height 12 cm and diameter 7 cm having a hemispherical shape on the top. The number of such cones to be filled with ice cream is
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 54
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The volume of the cylinder = πr2h = π × (22/7)2 × 38 = 8379π/2 cm3 The volume of the conical portion of Ice cream = 1/3πr2h = (1/3)π × (7/2)2 × 12 cm3 The volume of the hemispherical portion of Ice cream = (2/3)π × (7/2)3 cm3 The total volume of cone-shaped ice cream = π/3(49/4 × 12 + 343/4) cm3 = π/3(147 + 343/4) cm3 = π/3(588 + 343/4) cm3 = π/3 × 931/4 cm3 Number of cones = (8379π/2) × (12/931π) = 54. |