Question

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.
find the answer!if,I will mark you as brainlist!
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Answer 1

Gɪᴠᴇɴ :-

• Radius or conical Tent = 7m.
• Height = 24m.
• Width of cloth = 5m.
• Rate of Cloth = Rs.50/m (in Length).

Tᴏ Fɪɴᴅ :-

• Total Cost of cloth ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• CSA of Cone = π * radius * slant Height.
• Slant Height = √[radius² + height²]

Sᴏʟᴜᴛɪᴏɴ :-

Putting values in formula we get :-

→ slant height of conical tent = √(7² + 24²) = √(49 + 576) = √(625) = 25m.

So ,

→ CSA of conical Tent = (22/7) * 7 * 25 = 550m².

_________________

Now,

→ Area of cloth = 550m².

→ width of cloth = 5m.

→ Length of cloth = (Area/Width) = (550/5) = 110m.

_________________

Therefore,

→ cost of 1m cloth in Length = Rs.50

→ cost of 110m cloth in Length = 50 * 110 = Rs.5500 (Ans.)

Hence, Total Cost on Cloth was Rs.5500 .

Answer 2

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{1.8cm}\begin{picture}(16,4)\thicklines\put(8,1){\line(1,0){1}}\put(8,1){\line(1,2){1}}\put(10,1){\line(-1,2){1}}\put(9.03,1.6){\sf{24 m}}\put(9,1){\line(0,2){2}}\put(8.4,0.83){\sf{7 m}}\qbezier(8,1)(8.4,1.3)(9,1.3)\qbezier(9,1.3)(9.7,1.3)(10,1)\qbezier(8,1)(8.4,0.6)(9,0.6)\qbezier(9,0.6)(9.7,0.6)(10,1)\put(9.6,2){\sf l = \sqrt{\sf r^2 + h^2} }\end{picture}$

$\rule{120}{0.7}$

• Radius of Tent ( r ) = 7 m
• Height of Tent ( h ) = 24 m

⠀

✩ As, it formed right angle triangle inside of Cone. Hence Slant Height ( l ) will be 25 m by Pythagorean Triplet i.e. 7, 24 & 25.

✩ We make Tent on the Outer Surface of Cone only, so we need CSA of Tent only.

⠀

☢ $\underline{\textsf{Curved Surface Area of Conical Tent :}}$

$:\implies\sf CSA= \pi rl\\\\\\:\implies\sf CSA = \dfrac{22}{7} \times 7\:m \times 25\:m\\\\\\:\implies\sf CSA = 22 \times 25 \:m^2\\\\\\:\implies\sf CSA = 550 \:m^2$

$\rule{130}{1.2}$

✩ We need same cloth as of it's CSA i.e. 550 m², & we have already given width of cloth as 5 metre.

☢ $\underline{\textsf{Length of Cloth required will be :}}$

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

⠀

★ Cost of Cloth required will be :

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

⠀

$\therefore\:\underline{\textsf{Cost of the cloth required is \textbf{Rs. 5,500}}}.$