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Question

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A. 4567.67

B. 3873.33

C. 4066.67

D. 2345.98

Answer

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As we know that to find the volume of the frustum first, we had to find the area of its upper and lower base.

Now as we can see from the above figure that the lower and upper base of the frustum is in rectangle shape.

And the area of the rectangle is calculated as \[Area = Length \times Breadth\].

So, let the area of the upper base of the rectangle be \[{A_1}\].

So, \[{A_1} = 100 \times 10 = 1000{m^2}\]

And let the area of the lower base of the rectangle be \[{A_2}\].

So, \[{A_2} = 80 \times 8 = 640{m^2}\]

And it is given that the height (altitude) of the frustum is 5m.

So, now let us the put the values in the formula of volume of frustum that is \[\dfrac{h}{3}\left( {{A_1} + {A_2} + \sqrt {{A_1} \times {A_2}} } \right)\]

So, the volume of the frustum will be = \[ = \dfrac{5}{3}\left( {1000 + 640 + \sqrt {1000 \times 640} } \right) = \dfrac{5}{3}\left( {1640 + \sqrt {640000} } \right)\]

\[ \Rightarrow \]Volume = \[ = \dfrac{5}{3}\left( {1640 + 800} \right) = \dfrac{5}{3}\left( {2440} \right) = \dfrac{{12200}}{3} = 4066.66{m^3}\]