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The base edge of a regular pentagonal prism is 6 cm and its bases are 12 cm apart.

Find its volume in cubic centimeter.

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743.22

{cm}^{3}

786.89

{cm}^{3}

567.45

{cm}^{3}

842.12

{cm}^{3}

answer is A.

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Detailed Solution

Given measurements of a regular pentagonal prism
The base edge

(a)

= 6 cm
The height of the prism

(h)

= 12 cm
Volume of regular pentagonal prism = x (say)
According to the given value we have
Using the area of regular pentagon,

= \frac{1}{4} \sqrt{5 (5 + 2 \sqrt{5})} a^{2}

Substitute the value in this formula we obtain,

= \frac{1}{4} \sqrt{5 (5 + 2 \sqrt{5})} 6^{2}

= \frac{1}{4} \sqrt{25 + 10 \sqrt{5}} \times 36

= 9 \sqrt{47.36}

= 61.9367

Now we calculated the volume of prism,
Volume of prism = Base area x height

= 61.9367 \times 12

= 743.22 {cm}^{3}

Correct option is 1.

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