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Question

A frustum of a pyramid has an upper base $$100\ m$$ by $$10\ m$$ and a lower base of $$80\ m$$ by $$8\ m$$. if the altitude of the frustum is $$5\ m$$, find its volume (in cu. m).


A
4567.67
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B
3873.33
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C
4066.67
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D
2345.98
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Solution

The correct option is C $$4066.67$$
Give : Height of pyramid$$(h)=5\ m$$ 
It is a pyramid with rectangular base.
Edge of upper base $$length(L)=100\ m, breadth(B)=10\ m$$
Edge of lower base $$length(l)=80\ m, breadth(b)=8\ m$$
Area of upper base$$(A_{1})=L\times B=100\times 10 = 1000\ m^2$$
Area of lower base$$A_{2}=l\times b=640\ m^2$$
Volume of frustum$$(V)=\dfrac{h}{3}(A_{1} + A_2 + \sqrt{A_1 \times A_2})$$
$$\implies$$$$(V)=\dfrac{5}{3}(1000 + 640 + \sqrt{1000 \times 640})$$
                 $$=\dfrac{5}{3}(1640+800)=\dfrac{5}{3}(2440)=4066.666667$$
Hence, volume$$(V)=4066.67\ cu. m$$

Mathematics

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