Math, asked by Riyakabir, 1 year ago

The circumference of the base of a conical tent is 44 cm. If the height of tent is 24 cm, find the length of the canvas used in making the tent , if the width of the canvas is 2cm

Answers

Answered by sanketj
4

let r be the base radius.

height of the conical tent, h = 24 cm

length of the canvas required, if the width is 2 cm = ?

2\pi \: r = 44 \\ r =  \frac{44}{2\pi} \\ r =  \frac{44}{2  \times \frac{22}{7} }   \\ r =  \frac{44}{ \frac{44}{7} }  = ( \frac{44}{1} )( \frac{7}{44} ) \\ r = 7 \: cm

l =  \sqrt{ {r}^{2} +  {h}^{2}  } \\ l =  \sqrt{ {7}^{2}  +  {24}^{2} }  =  \sqrt{49 + 576}  =  \sqrt{625}  \\ l = 25 \: cm

Now, area of canvas required

= CSA of the tent

length \times width = \pi \: rl \\  l_{canvas}\times 2 =  \frac{22}{7}  \times 7 \times25 \\  l_{canvas}  =  \frac{22 \times 7 \times 25 }{7 \times 2}  = 25 \times 11 \\  l_{canvas} = 275 \: cm

Hence, length of the canvas required is 275 cm.

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