Fill in the blank:
The volume of a frustum cone top and bottom area of a circle and height is given. Choose the formula which satisfy the given statement ________________.( $A_{1}, A_{2}, h$ are area of top circle, area of bottom circle and height of frustum respectively).

\frac{1}{3} (A_{1} + A_{2} + \sqrt{A_{1} A_{2}}) h

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\frac{1}{3} (A_{1} - A_{2} + \sqrt{A_{1} A_{2}}) h

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\frac{1}{3} (A_{1} + A_{2} - \sqrt{A_{1} A_{2}}) h

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\frac{2}{3} (A_{1} + A_{2} + \sqrt{A_{1} A_{2}}) h

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Solution

The correct option is C $\frac{1}{3} (A_{1} + A_{2} + \sqrt{A_{1} A_{2}}) h$

Let radius of top & bottom be $r_{1}$ and $r_{2}$ & height be h.
Now, Area of top = $π r_{1}^{2} = A_{1}$
Area of bottom = $π r_{2}^{2} = A_{2}$
$∴$ Volume of frustum = $\frac{1}{3} (A_{1} + A_{2} + \sqrt{A_{1} A_{2}}) \times h$

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