Question

A conical tent has the area of its Base as 154m2 and that of its curved surface area is 550m2. Find the height of the tent.​

Answer 1

Solution ::

We have

Base area of a conical tent = 154${m}^{2}$

$\pi {r}^{2} = 154$

${r}^{2} = \frac{154}{\pi}$

${r}^{2} = \frac{154 \times 7}{22}$

$r = 49$

$r = \sqrt{49}$

$r = 7m$

And the Cusved surface area of the conical tent = 550${m}^{2}$

$\pi r l = 550$

$\frac{22}{7} \times 7 \times l = 550$

$22 \times l = 550$

$l = \frac{550}{22}$

$l = 25m$

Now =》

${l}^{2} = {h}^{2} + {r}^{2}$

${h}^{2} = {l}^{2} - {r}^{2}$

${h}^{2} = {25}^{2} - {7}^{2}$

${h}^{2} = 652 - 49$

${h}^{2} = 576$

$h = \sqrt{576}$

$h = 24m \: \: \: \: \: \: \: \: \: \: \: \: \: ans$

Hence, the height of the conical tent = 24 metres.