Question

The capacity of a closed cylindrical vessel of height 1m is15.4liter how many m2 of metal sheet would needed to make it?​

Answer 1

$\huge\mathcal{\boxed{\fcolorbox{lime}{yellow}{SOLUTION}}}$

☃️ Height of the vessel = 1m

☃️ Capacity of the vessel = 15.4 liters

• 15.4 L = 0.0154 m³

⭐ Volume of the cylindrical vessel = πr²h

→ 0.0154 = 22/7 × r² × 1

→ r² = 0.0049

→ r = 0.07 m

✨ Metal sheet needed to make the cylindrical vessel = T.S.A of the cylindrical vessel .

$\bf{\implies\:2\:\pi\:r\:(r\:+\:h)\:}$

$\bf{\implies\:2\times{\dfrac{22}{7}}\times{0.07}\:(0.07\:+\:1)\:}$

$\bf\green{\implies\:0.4708\:m^2}$

∴ 0.4708m² of sheet will be required to make the vessel .

Answer 2

$\huge{\underline{\sf{\green{Solution-}}}}$

$\underline\green{\sf Given -}$

$\longrightarrow \sf{h = 1m}$

$\longrightarrow \sf{Volume = 15.4 l}$

$\underline\green{\sf Find -}$ TSA?

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Volume of Cylinder = $\huge{\underline{\sf{\green{\pi{r}^{2}h}}}}$

$\longrightarrow \sf{\pi{r}^{2}h \: = \: 1.54\times1000}$

$\longrightarrow \sf{= \dfrac{22}{7}\times{r}^{2}\times(100) = 1.54\times1000}$

$\longrightarrow \sf{{r}^{2} = \dfrac{1.54 \: \times \: 1000 \: \times 7} {22 \: \times 100}}$

$\longrightarrow \sf{{r}^{2}= 49}$

$\longrightarrow \sf{r = \sqrt{49}}$

$\longrightarrow \sf\green{r = 7cm}$

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TSA of cylinder = $\huge{\underline{\sf{\green{2 \pi r(r+h)}}}}$

$\longrightarrow \sf{=2\times\dfrac{22}{7}(7+100)}$

$\longrightarrow \sf{=44\times107}$

$\longrightarrow \sf\green{= 4708{cm}^{2}}$

$: 4708{cm}^{2} = ?{m}{2}$

$\longrightarrow \sf{\dfrac{4708}{100\times100}{m}^{2}}$

$\longrightarrow \sf\green{ = 0.4708{m}^{2}}$

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