Question

The radius and perpendicular height of a cone are in the ratio 1:3 . If the volume of the cone is 84.857 cm³ , find perpendicular height.

Answer 1

$\textbf{\huge{ANSWER:}}$

Volume of a cone = $\pi r^{2} h \times \frac{1}{3}$

Given:

Radius : Perpendicular height = 1 : 3

Let the radius be = x
Perpendicular height = 3x

Put the values in the formula;

=》 84.857 = $\pi \times x^{2} \times 3x \times \frac{1}{3}$

=》 84.857 = $\pi \times x^{2} \times x$

=》 84.857 = $\pi \times x^{3}$

=》 $\frac{84.857 \times 7}{22} = x^{3}$

=》 $\textbf{x = 3 cm}$ (approx)

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