The volume of a right circular cone is equal to the volume of that right circular cylinder whose height is 27 cm and diameter of its base is 30 cm. If the height of the cone is 25 cm, then what will be the diameter of its base?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 54 cm.
| Understanding/Application |
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Height of the cylinder = 27 cm Radius of the cylinder = 30/2 = 15 cm Volume of the cylinder = πr2h = π × 152 × 27 Height of the cone = 25 cm Let radius of the cone be r cm. Volume of the cone = πr2h/3 = (πr2 × 25)/3 |
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Volumes of the cone and cylinder are equal. π × 152 × 27 = (πr2 × 25)/3 152 × 81 = r2 × 52 (152 × 92)/52 = r2 r = (15 × 9)/5 = 27 cm Diameter of the cone = 2r = 2(27) = 54 cm |