The radius and the height of right circular cone are in the ratio $5 : 12$ If its volume is $314$ cubic m. Find the diameter of its base $(π = 31.4)$ .

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Solution

Let the radius and height be $5 x$ and $12 x$ , respectively.

$∴$ Volume of the cone
$= \frac{1}{3} \times (3.14) \times {(5 x)}^{2} \times (12 x)$ $= 314 x^{3}$ .

Given, volume $= 314 m^{3}$
Thus $314 x^{3} = 314$
$⟹$ $x^{3} = 1$ $⟹$ $x = 1$

Then, radius $= 5 (1) = 5 m$ .
Therefore, Diameter $= 2 r = 2 \times 5 = 10 m$ .

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The radius and the height of right circular cone are in the ratio 5:12 If its volume is 314 cubic m. Find the diameter of its base (π=31.4).

Let the radius and height be 5x and 12x, respectively.∴ Volume of the cone =13×(3.14)×(5x)2×(12x) =314x3.Given, volume =314m3Thus 314x3=314⟹ x3=1 ⟹ x=1Then, radius =5(1)=5m.Therefore, Diameter =2r=2×5=10m.

The radius and the height of right circular cone are in the ratio $5 : 12$ If its volume is $314$ cubic m. Find the diameter of its base $(π = 31.4)$ .