The ratio of the perpendicular height and the slant height of a right circular cone is given as 4 : 5 and the volume of the cone is given as 12936 cm³. Find the radius (in cm) of the base of the given cone. (Use π = 22/7)
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Correct answer: D
Explanation
The correct answer is option 4 i.e 21.
Let h = 4x and l = 5x
Using Pythagoras theorem: l2 = r2 + h2
⇒ (5x)2 = r2 + (4x)2
⇒ 25x2 = r2 + 16x2
⇒ r2 = 9x2
⇒ r = 3x
Volume (V) = 12936 cm3
⇒ 1/3πr2h = 12936 ⇒ 1/3 × 22/7 × (3x)2 × 4x = 12936 ⇒ 1/3 × 22/7 × 9x2 × 4x = 12936
⇒ 264x3 / 7 = 12936 ⇒ x3 = (12936 × 7) / 264 ⇒ x3 = 343 ⇒ x = 7
r = 3x = 3 × 7 = 21 cm