Question

UCU Q-21 If the cone-shaped tent is 10 m high and its base radius is 24 m, then (1) Find the slant height of the tent. (ii) Cost of the canvas required to make the tent, if the cost of 1m² canvas is * 70. 3​

Answer 1

$\large \sf \underline{Solution-}$

Here it is given that,

➢ Height (h) of the conical tent = 10 m

➢ Radius (r) of the conical tent = 24 m

Let,

➢ The slant height of the tent be (l)

Then,

$\rm \implies \: l^{2} = r^{2} + h^{2}$

$\rm \implies \: l^{2} = 24^{2} + 10^{2}$

$\rm \implies \: l^{2} = 576 + 100$

$\rm \implies \: l^{2} = 676$

$\rm \implies \: l = \sqrt{676}$

$\rm \implies \: l = 26 \: m$

Therefore,

➢ Slant height of the conical tent = 26 m

Here,

The tent does not cover the base, so we find the curved surface area of the tent.

So,

➢ Curved surface area of tent = πrl

• We have, l = 26 m and r = 24 m

Substitute the values,

$\rm \implies \left( \dfrac{22}{7} \times 24 \times 26 \right) \: m ^{2}$

$\rm \implies \left( \dfrac{22 \times 24 \times 26}{7} \right) \: m ^{2}$

$\rm \implies \dfrac{13728}{7} \: m ^{2}$

We have,

➢ Cost of 1m² canvas = Rs. 70

Now,

Total cost of canvas = Total curved surface area × Cost per m²

$\rm \implies Rs. \: \left(\dfrac{13728}{7} \times 70\right)$

$\rm \implies Rs. \: 137280$

Thus, total amount required to construct the tent = Rs. 137280