Question

$\large{ \bf{Question :-}}$

Meera has a piece of canvas whose area is 551 m2. She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 m2, find the volume of the tent that can be made with it.
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Answer 1

$\star \; {\underline{\boxed{\pmb{\orange{\frak{ \; Given \; :- }}}}}}$

• Area of Canvas = 551 m²
• Wastage = 1 m²
• Radius of Base = 7 m

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$\star \; {\underline{\boxed{\pmb{\color{darkblue}{\frak{ \; To \; Find \; :- }}}}}}$

• Volume of the Tent = ?

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$\star \; {\underline{\boxed{\pmb{\pink{\frak{ \; SolutioN \; :- }}}}}}$

$\maltese \; {\underline{\textbf{\textsf{ Formula \; Used \; :- }}}}$

• ${\underline{\boxed{\pmb{\sf{ Curved \; Surface \; Area = \pi r l }}}}}$

• ${\underline{\boxed{\pmb{\sf{ Volume = \dfrac{1}{3} \pi {r}^{2} h }}}}}$

Where :

• $\sf{ \pi = \dfrac{22}{7} }$

• r = Radius
• l = Slant Height
• h = Height

$\maltese \; {\underline{\textbf{\textsf{ Original \; Surface \; Area \; :- }}}}$

${\longmapsto{\qquad{\sf{ Original \; CSA = Area - Wastage }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ Original \; CSA = 551 - 1 }}}} \\ \\ \\ \ {\qquad \; \; {\longmapsto{\underline{\boxed{\pmb{\sf{ Original \; CSA = 550 \; {m}^{2} }}}}}}} \; {\red{\bigstar}}$

$\maltese \; {\underline{\textbf{\textsf{ Slant \; Height \; :- }}}}$

${\implies{\qquad{\sf{ CSA = \pi rl }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ 550 = \dfrac{22}{7} \times 7 \times l }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ 550 = \dfrac{22}{\cancel7} \times \cancel7 \times l }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ 550 = 22 \times l }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ \dfrac{550}{22} = l }}}} \\ \\ \\ \ {\implies{\qquad{\sf{ \cancel\dfrac{550}{22} = l }}}} \\ \\ \\ \ {\qquad \; \; {\implies{\underline{\boxed{\pmb{\sf{ Slant \; Height = 25 \; m }}}}}}} \; {\purple{\bigstar}}$

$\maltese \; {\underline{\textbf{\textsf{ Height \; :- }}}}$

${\dashrightarrow{\qquad{\sf{ {Slant \; Height}^{2} = {Height}^{2} + {Radius}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ {25}^{2} = {Height}^{2} + {7}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 625 = {Height}^{2} + 49 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 625 - 49 = {Height}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 576 = {Height}^{2} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \sqrt{576} = Height }}}} \\ \\ \\ \ {\qquad \; \; {\dashrightarrow{\underline{\boxed{\pmb{\sf{ Height = 24 \; m }}}}}}} \; {\color{maroon}{\bigstar}}$

$\maltese \; {\underline{\textbf{\textsf{ Volume \; of \; Tent \; :- }}}}$

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { Volume = \dfrac{1}{3} \pi {r}^{2} h } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { Volume = \dfrac{1}{3} \times \dfrac{22}{7} \times {7}^{2} \times 24 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { Volume = \dfrac{1}{3} \times \dfrac{22}{\cancel7} \times \cancel{49} \times 24 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { Volume = \dfrac{1}{3} \times 22 \times 7 \times 24 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { Volume = \dfrac{1}{\cancel3} \times 22 \times 7 \times \cancel{24} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { Volume = 1 \times 22 \times 7 \times 8 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; \sf { Volume = 22 \times 56 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longmapsto \; \; {\underline{\boxed{\pmb{\sf{ Volume = 1232 \; {m}^{3} }}}}} \; {\green{\bigstar}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Volume of the tent is 1232 m³ .

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Answer 2

Step-by-step explanation:

Volume of the tent is 1232 m³

it's Isha