The volume of a frustum cone is $4, 200 c m^{3}$ , whose base and upper area of a circle is $10 c m^{2}$ and $90 c m^{2}$ . Find the height of the cone.

67

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77

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87

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97

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Solution

The correct option is D $97$
Volume of a frustum cone = $\frac{1}{3} (A_{1} + A_{2} + \sqrt{A_{1} A_{2}}) h$
$4200 = \frac{1}{3} (90 + 10 + \sqrt{90 \times 10}) h$
$4200 = \frac{1}{3} (100 + 30) h$
$\frac{4200}{43.33} = h$
$h \approx 97$ cm

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