There is a pyramid on a base which is a regular hexagon of side 2a- If every slant edge of this pyramid is of length 5 a -2 then the volume of this pyramid must be-A- 3 a 3-3B- 3 a 3C- 3 a 3-2D- 6 a 3

The correct option is A 3a^3√(3)Volume of the pyramid = √(3)/2 (2a)^2 h (h:pyramid height) h^2 + (2a)^2 = (5a/2)^2 h = 3a/2 Volume of the pyramid = 3√(3)a^3 ...

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There is a py...

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There is a pyramid on a base which is a regular hexagon of side 2a. If every slant edge of this pyramid is of length $\frac{(5 a)}{2}$ then the volume of this pyramid must be:

3 a^{3}

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3 a^{3} \sqrt{2}

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3 a^{3} \sqrt{3}

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6 a^{3}

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Solution

The correct option is C $3 a^{3} \sqrt{3}$
$V o l u m e o f t h e p y r a m i d = \frac{\sqrt{3}}{2} (2 a)^{2} h (h : p y r a m i d h e i g h t)$
$h^{2} + (2 a)^{2} = (\frac{5 a}{2})^{2}$
$h = \frac{3 a}{2}$
$V o l u m e o f t h e p y r a m i d = 3 \sqrt{3} a^{3}$

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There is a pyramid on a base which is a regular hexagon of side 2a. If every slant edge of this pyramid is of length (5a)2 then the volume of this pyramid must be:

The correct option is C 3a3√3Volume of the pyramid = √32(2a)2h(h:pyramid height) h2+(2a)2=(5a2)2 h=3a2 Volume of the pyramid = 3√3a3

There is a pyramid on a base which is a regular hexagon of side 2a. If every slant edge of this pyramid is of length $\frac{(5 a)}{2}$ then the volume of this pyramid must be:

The correct option is C $3 a^{3} \sqrt{3}$
$V o l u m e o f t h e p y r a m i d = \frac{\sqrt{3}}{2} (2 a)^{2} h (h : p y r a m i d h e i g h t)$
$h^{2} + (2 a)^{2} = (\frac{5 a}{2})^{2}$
$h = \frac{3 a}{2}$
$V o l u m e o f t h e p y r a m i d = 3 \sqrt{3} a^{3}$