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Q.

The base edge of a regular hexagonal prism is 6 cm and its bases are 12 cm apart. Find its volume in cu. cm

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a

1563.45

cu . cm

b

1058.45

cu . cm

c

1896.37

cu . cm

d

1122.37

cu . cm

answer is D.

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Detailed Solution

Given,
Base edge of height is 12 cm.
And length of sides = 6 cm.
All the 6 sides of a regular hexagon is the same in measure.
Thus, the base of the prism has six sides, there will be a total of six equilateral triangles.
One equilateral triangle's surface area

= \frac{\sqrt{3}}{4} \times {side}^{2}

= \frac{\sqrt{3}}{4} \times 36

= 9 \sqrt{3}

Therefore,
Six equilateral triangle's surface area

= 6 \times 9 \sqrt{3}

= 54 \sqrt{3}

So, the base area of prism

= 54 \sqrt{3} sq . cm

Prism’s volume = base × height

= 54 \sqrt{3} \times 12

= 1122.37 cu . cm

So, the correct option is 4.

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