The base of a right prism is an equilateral triangle of side $6$ m. If its volume is $81 \sqrt{3} m^{3}$ , find the height of the prism.

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Solution

Given: $a = 6$ m, $V = 81 \sqrt{3} c m^{3}$ , we have to find h. We know that
$V = B \times h$ , and $B = \frac{\sqrt{3}}{2} a^{2} = \frac{\sqrt{3}}{4} \times 6 \times 6 = 9 \sqrt{3}$ .
Thus we obtain $81 \sqrt{3} = 9 \sqrt{3} \times h$ .
Hence $h = 9$ m.

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The base of a right prism is an equilateral triangle of side 6m. If its volume is 81√3m3, find the height of the prism.

Given: a=6m, V=81√3cm3, we have to find h. We know that V=B×h, and B=√32a2=√34×6×6=9√3.Thus we obtain 81√3=9√3×h.Hence h=9m.

The base of a right prism is an equilateral triangle of side $6$ m. If its volume is $81 \sqrt{3} m^{3}$ , find the height of the prism.

Given: $a = 6$ m, $V = 81 \sqrt{3} c m^{3}$ , we have to find h. We know that
$V = B \times h$ , and $B = \frac{\sqrt{3}}{2} a^{2} = \frac{\sqrt{3}}{4} \times 6 \times 6 = 9 \sqrt{3}$ .
Thus we obtain $81 \sqrt{3} = 9 \sqrt{3} \times h$ .
Hence $h = 9$ m.