Question

Here's your question of the day♥️ A conical tent of radius 7m and height 24m is to be made.find the cost of the 5m wide cloth required at the rate of rs 50 per m.

Answer 1

$\huge\sf\pink{Answer}$

☞ Cost of cloth required = 5500

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$\huge\sf\blue{Given}$

✭ A conical tent of radius 7 m and height 24 m

✭ Width = 5 m

✭ Cost = 50 per m

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$\huge\sf\gray{To \:Find}$

◈ Cost to buy the cloth?

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$\huge\sf\purple{Steps}$

$\large\sf\star \: Diagram \:\star$

$\setlength{\unitlength}{2.00cm}\begin{picture}(16,4)\thicklines\put(8,1){\line(1,0){1}}\put(8,1){\line(1,2){1}}\put(10,1){\line(-1,2){1}}\put(9.03,1.6){\sf{24 m}}\put(9,1){\line(0,2){2}}\put(8.4,0.83){\sf{7 m}}\qbezier(8,1)(8.4,1.3)(9,1.3)\qbezier(9,1.3)(9.7,1.3)(10,1)\qbezier(8,1)(8.4,0.6)(9,0.6)\qbezier(9,0.6)(9.7,0.6)(10,1)\put(9.6,2){\sf l = \sqrt{\sf r^2 + h^2} }\end{picture}$

CSA of conical tent is given by,

$\underline{\boxed{\sf CSA= \pi rl}}$

Substituting the given values,

$\twoheadrightarrow\sf CSA = \dfrac{22}{7} \times 7\:m \times 25\:m\\\\ \twoheadrightarrow\sf CSA = 22 \times 25 \:m^2\\\\ \red{\twoheadrightarrow\sf CSA = 550 \:m^2}$

Now, the Length of the cloth required will be,

$\rightarrowtail\sf Area\:of\:Cloth=CSA_{(Cone)}\\\\ \rightarrowtail\sf Length \times Width=550\:m^2\\\\\rightarrowtail\sf Length \times 5\:m=550\:m^2\\\\ \rightarrowtail\sf Length=\dfrac{550\:m^2}{5\:m}\\\\\green{\rightarrowtail\sf Length = 110 \:m}$

And finally the Cost of the Cloth required will be,

$\dashrightarrow\sf\:\:Cost=Length\:of\: Cloth \times Rate\\\\\dashrightarrow\sf\:\:Cost=110\:m \times Rs.\:50\:m^{-1}\\\\\dashrightarrow\sf\:\:Cost=110 \times Rs.\:50\\\\\dashrightarrow{\orange{\sf{\:Cost = Rs.5,500}}}$

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Answer 2

Answer:

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