Question

how many metre of cloth 5 m wide will be required to make a conical tent of base radius 7m and height 24 m? also, find the cost of the cloth at the rate of rs.45 per metre​

Answer 1

AnswEr :

$\textsf{As we have to find the Cloth Required for} \\ \textsf{Conical Tent, then we will find Curved} \\ \textsf{Surface Area of Cone i.e.}\sf\:(\pi rl)$

• Radius ( r ) = 7 m
• Height ( h ) = 24 m
• Width of Cloth = 5 m

$\rule{170}{1}$

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$:\implies\tt CSA = \pi rl\\\\\\:\implies\tt CSA = \pi r \times \sqrt{r^2 + h^2}\\\\\\:\implies\tt CSA = \dfrac{22}{7} \times 7 \times \sqrt{(7)^2 +(24)^2}\\\\\\:\implies\tt CSA = 22 \times \sqrt{49 + 576}\\\\\\:\implies\tt CSA = 22 \times \sqrt{625}\\\\\\:\implies\tt CSA = 22 \times \sqrt{25 \times 25}\\\\\\:\implies\tt CSA = 22 \times 25\\\\\\:\implies\tt CSA = 550 \:m^2$

$\rule{200}{2}$

$\underline{\bigstar\:\textsf{Cost of Cloth for Conical Tent :}}$

$\longrightarrow\tt Cost = Length\:of\:Cloth \times Rate\\\\\\\longrightarrow\tt Cost = \dfrac{Area\:of\:Tent}{Width\:of\:Cloth} \times Rate\\\\\\\longrightarrow\tt Cost = \dfrac{550m^2}{5m} \times Rs. 45\\\\\\\longrightarrow\tt Cost = 110 \:m \times Rs. 45\\\\\\\longrightarrow\boxed{\blue{\tt Cost = Rs. 4950}}$

⠀

∴ Length of Cloth Required is 110 metre, and it will Cost Rs. 4950 to make tent.

Answer 2

$\huge{\blue{\mathbb{A}}}\blue{\mathfrak{nswer}}$

Firstly, we will find the value of the l.

$\large{\red{\boxed{\sf{l = \sqrt{h^2 + r^2}}}}}$

$\sf{l = \sqrt{24^2 + 7^2}} \\ \\ \sf{→l = \sqrt{576 + 49}} \\ \\ \sf{→l = \sqrt{625}} \\ \\ \sf{→l = (\sqrt{25})^2} \\ \\ \sf{→l = 25}$

Now,

$\boxed{\sf{\green{C.S.A = \pi r l}}}$

$\sf{→C.S.A = \frac{22}{\cancel{7}}\times \cancel{7} \times 25} \\ \\ \sf{→C.S.A = 22 \times 25} \\ \\ \sf{→C.S.A = 550 \: m^2}$

$\rule{200}{2}$

As, we have to find the Cost.

So,

$\boxed{\sf{Cost = \frac{C.S.A \: of \: cone}{Width \: of \: cloth} \times Rate}}$

(Putting Values)

$\sf{→Cost = \frac{\cancel{550}}{\cancel{5}} \times 45} \\ \\ \sf{→Cost = 110 \times 45} \\ \\ \sf{→Cost = Rs. \: 4950}$

$\implies{\purple{\boxed{\sf{Cost = Rs. \: 4950}}}}$