Question

the cost of canvas required to make the conical tent of base radius 7m at the rate of 8m² is rs 4400/- find the height of tent​

Answer 1

Given :

• Base radius of conical tent, r = 7 m
• Cost of canvas per m² = Rs. 8
• Total cost = Rs. 4400

To Find :

• Height of tent = ?

Solution :

As the total cost to make the tent is Rs. 4400 at the rate of Rs. 8 per m²,

$\sf So, \: LSA = \dfrac{Rs. \: 4400}{Rs. \: 8 \: per \: m^{2}}$

$\sf : \implies \: LSA = \dfrac{\cancel{4400}^{550}}{\cancel{8}} \: m^{2}$

$\sf : \implies \: LSA = 550 \: m^{2}$

Now, we know that LSA of cone is :

$\large \underline{\boxed{\sf{LSA = \pi r l}}}$

Here, l is slant height, which is equal to

$\large \underline{\boxed{\sf{l = \sqrt{h^{2} + r^{2}}}}}$

Therefore,

$\large \underline{\boxed{\sf{LSA = \pi r \times \sqrt{h^{2} + r^{2}}}}}$

$\sf : \implies \: 550 = \dfrac{22}{7} \times 7 \times \sqrt{h^{2} + (7)^{2}}$

$\sf : \implies \: 550 = \dfrac{22}{\cancel{7}} \times \cancel{7} \times \sqrt{h^{2} + 49}$

$\sf : \implies \: 550 = 22 \times \sqrt{h^{2} + 49}$

$\sf : \implies \: \dfrac{\cancel{550}^{25}}{\cancel{22}} = \sqrt{h^{2} + 49}$

$\sf : \implies \: 25 = \sqrt{h^{2} + 49}$

By squaring both sides,

$\sf : \implies \: (25)^{2} = (\sqrt{h^{2} + 49})^{2}$

$\sf : \implies \: 625 = h^{2} + 49$

$\sf : \implies \: 625 - 49 = h^{2}$

$\sf : \implies \: 576 = h^{2}$

$\sf : \implies \: h^{2} = 576$

$\sf : \implies \: h = \sqrt{576}$

$\sf : \implies \: h = \sqrt{(24)^{2}}$

$\sf : \implies \: h = 24$

$\large \underline{\boxed{\sf h = 24 \: m}}$

Hence, height of conical tent = 24 m