The semi vertical angle of a right circular cone is $30^{0}$ . If the height of the cone is 6.125 cm, then the approximate value of the volume of the cone ( in cubic cm ) is

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$(23.5) π$

$48 π$

$(76.5) π$

$(25.5) π$

answer is D.

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Detailed Solution

$\begin{array}{rcl} \tan 30^{\circ} & = & \frac{r}{h} \\ r & = & \frac{h}{\sqrt{3}} \\ v & = & \frac{1}{3} {πr}^{2} h = \frac{1}{3} π \frac{h^{2}}{3} . h = \frac{π}{9} h^{3} = (25.5) π \end{array}$

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