Question

How many meters of clothes, 5m wide, will be required to make a conical tent, the radius of whose base is 7m and hight, H =24m.

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Answer 1

Given :

• Width of cloth = 5 m
• Radius of tent = 7 m
• Height of tent = 24 m

$\\ \rule{200pt}{3pt}$

To Find :

• Length of cloth = ?

$\\ \rule{200pt}{3pt}$

Solution :

~ ${\underline{\pmb{\frak{ Formula \; Used \; :- }}}}$

• ${\underline{\boxed{\pink{\sf{ Curved \; Surface \; Area{\small_{(Cone)}} = \pi rl }}}}}$

• ${\underline{\boxed{\pink{\sf{ Total \; Area{\small_{(Rectangle)}} = Length \times Breadth }}}}}$

Where :

• ➟ ${\sf{ \pi = \dfrac{22}{7} }}$

• ➟ r = Radius
• ➟ l = Slant Height

$\\ \qquad{\rule{150pt}{1pt}}$

~ ${\underline{\pmb{\frak{ Calculating \; the \; Slant \; Height \; :- }}}}$

${\longmapsto{\qquad{\sf{ {Slant \; Height}^{2} = {Radius}^{2} + {Height}^{2} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ {Slant \; Height}^{2} = {7}^{2} + {24}^{2} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ {Slant \; Height}^{2} = 49 + 576 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ {Slant \; Height}^{2} = 625 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Slant \; Height = \sqrt{625} }}}} \\ \\ \ {\qquad{\orange{\sf{ Slant \; Height \; of \; the \; tent = 25 \; m }}}}$

~ ${\underline{\pmb{\frak{ Calculating \; the \; Surface \; Area \; of \; Tent \; :- }}}}$

$\begin{gathered} \implies \; \; \sf { Surface \; Area = \pi rl } \\ \end{gathered}$

$\begin{gathered} \implies \; \; \sf { Surface \; Area = \dfrac{22}{7} \times 7 \times 25 } \\ \end{gathered}$

$\begin{gathered} \implies \; \; \sf { Surface \; Area = \dfrac{22}{\cancel7} \times \cancel7 \times 25 } \\ \end{gathered}$

$\begin{gathered} \implies \; \; \sf { Surface \; Area = 22 \times 25 } \\ \end{gathered}$

$\begin{gathered} \implies \; \; {\qquad{\green{\sf{ Surface \; Area \; of \; Tent = 550 \; {m}^{2} }}}} \\ \end{gathered}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ ${\underline{\pmb{\frak{ Calculating \; the \; Length \; of \; Cloth \; :- }}}}$

$\begin{gathered} \dashrightarrow \; \; \sf { Surface \; Area{\small_{(Tent)}} = Length \times Breadth } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 550 = Length \times 5 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \dfrac{550}{5} = Length } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \cancel\dfrac{550}{5} = Length } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; {\qquad{\red{\sf{ Length \; of \; the \; Cloth = 110 \; m }}}} \\ \end{gathered}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ ${\underline{\pmb{\frak{ Therefore \; :- }}}}$

❛❛ Length of the cloth required is 110 m .❜❜

$\\ {\underline{\rule{300pt}{9pt}}}$

Answer 2

To Find :

Length of cloth = ?

\begin{gathered} \\ \rule{200pt}{3pt} \end{gathered}

Given :

Width of cloth = 5 mRadius of tent = 7 mHeight of tent = 24 m

\begin{gathered} \\ \rule{200pt}{3pt} \end{gathered}