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Q.

If volume of an equilateral triangle-based prism is $72 \sqrt{3} m^{3}$ and height is 7 m, find the length of the base.

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a

\frac{12}{\sqrt{7}} m

b

\frac{11}{\sqrt{7}} m

c

\frac{10}{\sqrt{7}} m

d

\frac{09}{\sqrt{7}} m

answer is A.

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Detailed Solution

Given,
Volume of the prism

V = 72 \sqrt{3} m^{2}

The height

h = 7 m

Formula for volume of prism

V = Bh

(B = base area)

72 \sqrt{3} = B \times 7

B = \frac{72 \sqrt{3}}{7}

So, the base area B in term of side

s

can be given as,,

B = \frac{\sqrt{3}}{2} s^{2}

\frac{72 \sqrt{3}}{7} = \frac{\sqrt{3}}{2} s^{2}

s^{2} = \frac{72 \times 2}{7}

s^{2} = \frac{144}{7}

s = \sqrt{\frac{144}{7}}

s = \frac{12}{\sqrt{7}}

So, base length =

\frac{12}{\sqrt{7}} m

.
Correct option is 1.

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