Q5 of 44 Page 14

The radius and height of a right circular cone are in the ratio of 5:12. If its volume is 314 cm3, find its slant height.

[Take π=3.14]

Given: Volume of a right circular cone = 314cm3


and r : h = 5 : 12


Let r = 5x and h = 12x


The volume of a right circular cone





⇒ x3 = 1


Hence, x = 1


∴ r = 5x = 5×1 = 5cm


and h = 12x = 12×1 = 12cm


Now, we have to find the slant height, l


Slant height, l = √(r2 + h2)


= √{(5)2 + (12)2}


= √25+144


= √169


= ±13


= 13cm


[taking positive root, because slant height can’t be negative]


∴ Slant Height = 13cm


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