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प्रश्न
If the ratio of radius of base and height of a cone is 5:12 and its volume is 314 cubic metre. Find its perpendicular height and slant height. (π = 3.14)
उत्तर
The ratio of radius of base and perpendicular height of a cone is 5 : 12.
Let the radius of base and perpendicular height of the cone be 5x and 12x, respectively.
Volume of the cone = 314 m3
∴ `1/3`πr2h = 314 m3
⇒ `1/3 xx 3.14 xx (5x)^2 xx 12x` = 314
⇒ 314 x3 = 314
⇒ x3 = 1
⇒ x = 1
∴ Perpendicular height of the cone = 12x = 12 × 1 = 12 m
Radius of the cone = 5x = 5 × 1 = 5 m
Now,
l2 = r2 + h2
⇒ l2 = (12)2 + (5)2
⇒ l2 = 144 + 25
⇒ l2 = 169
⇒ l2 = (13)2
⇒ l = 13 m
Thus, the perpendicular height and slant height of the cone is 12 m and 13 m, respectively.
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