Question

A conical tent is 10 m high and the radius of the base is 24 m. Find
(i) the slant height of the tent.
(ii) the cost of the canvas required to make the tent, if the cost of 1 m^2 canvas is Rs. 70.


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Answer 1

We have, Height of the tent, h=10 m

Radius of base, r=24 m

(i) Slant height,l=?

l²=h²+r²

l²=10²+24²

l²= 100+576

l²=676

l= ±26

Height can not be negative.

Therefore, the slant height of the tent is 26m.

(ii) Area of the canvas required= CSA of cone=πrl

$\: \: \: \: \: \: \: \: \: = \frac{22}{7} \times 24 \times 26 \\ \: \: \: \: \: \: \: \: \: = \frac{13728}{7} {m}^{2}$

The cost of 1 m² of canvas= ₹ 70

Total cost of canvas=₹(70×13728/7)=₹ 137280

Answer 2

Step-by-step explanation:

We have, Height of the tent, h=10 m

Radius of base, r=24 m

(i) Slant height,l=?

l²=h²+r²

l²=10²+24²

l²= 100+576

l²=676

l= ±26

Height can not be negative.

Therefore, the slant height of the tent is 26m.

(ii) Area of the canvas required= CSA of cone=πrl

\begin{lgathered}\: \: \: \: \: \: \: \: \: = \frac{22}{7} \times 24 \times 26 \\ \: \: \: \: \: \: \: \: \: = \frac{13728}{7} {m}^{2}\end{lgathered}

=

7

22

×24×26

=

7

13728

m

2

The cost of 1 m² of canvas= ₹ 70

Total cost of canvas=₹(70×13728/7)=₹ 137280