Q.To make a vertical circular conical tent, \(188\frac{4}{7}\) square meters of cloth is required. If the base perimeter of the tent is \(37\frac{5}{7}\) meters, then what are the slant height, radius, and height of the tent?

Let the slant height, radius, and height of the tent be \(l\) meters, \(r\) meters, and \(h\) meters respectively. ∴ According to the question, \(2\pi r = 37\frac{5}{7}\) Or, \(2 \times \frac{22}{7} \cdot r = \frac{264}{7}\) Or, \(r = \frac{264 \times 7}{7 \times 2 \times 22}\) Or, \(r = 6\) Again, according to the question, \(\pi r l = 188\frac{4}{7}\) Or, \(\frac{22}{7} \times 6 \times l = \frac{1320}{7}\) Or, \(l = \frac{1320}{\frac{22}{7} \times 6} = 10\) Again, \(h^2 = l^2 - r^2\) Or, \(h^2 = 10^2 - 6^2\) Or, \(h^2 = 100 - 36 = 64\) Or, \(h = \sqrt{64} = 8\) ∴ The slant height, radius, and height of the tent are 10 meters, 6 meters, and 8 meters respectively.
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