Question

the radius of the conical lent is 7cm and the height is 24 cm calculate the length of the Canvas used in making the tent if width of the rectangular canvas is 4m​

Answer 1

$\huge \mathscr{\orange {\underline{\pink{\underline {Answer:-}}}}}$

Area of the canvas = Curved surface area of the conical tent

Since the canvas is rectangular in shape, its area is = Length × width

Curved surface area of a cone =πrL, where r is the radius of the cone and l is the slant height.

For a cone, L=√h²+r2², where l is the slant height.

Hence,

 L=√24²+7²

⇒L=√625

⇒L=25 cm

Hence,

Length × 5 = 722×7×25

∴ length = 110 m.

Answer 2

Answer:

GIVEN :-

• Radius of conical tent = 7cm
• Height of tent = 24 cm
• Width of rectangular canvas 4 m= 400 cm

TO FIND :-

• Length of rectangular canvas = ?

SOLUTION :-

• we know that if we are making a conical tent then we should take only Curve surface area of Tent .

• For finding the curve surface of cone we have to calculate the value of Slant height.

$\sf \: Slant height ( l ) = \sqrt{ (radius) {}^{2} + (height) ^{2} }$

$\sf \: ( l ) = \sqrt{ ( {7)}^{2} + (24) ^{2} }$

$\implies \sf \: ( l ) = \sqrt{ 49 + 576 }$

$\implies \sf \: ( l ) = \sqrt{ 625}$

$\implies \sf \: ( l ) = 25 \: \: cm$

$\sf \: NOW \: \: Curved \: surface \: \: area \: \: of \: cone =\pi rl$

$\sf \: = \frac{22}{7} (7)(25)$

$= \sf \: 22 \times 25$

$\sf = 550 \: {cm}^{2}$

• This area must be equal to the area of rectangular canvas.
• Let the length of canvas is L cm
• width of canvas w =400 cm

$\sf \: Area \: of \: canvas \: = length \times width$

$\sf \: Area \: of \: canvas \: = L \times 400 \: {cm}^{2}$

• Now area of canvas is equal to the area of tent

$\sf \: Area \: of \: canvas \: = area \: of \: tent$

$\implies\sf \: L \times 400 \: = 550$

$\implies\sf \: L \: = \frac{550}{400}$

$\pink{ \implies\sf \: L \: = \frac{11}{8} \: \: cm}$