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

Answer:

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

πr

2

h

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

2

h=1.54×1000

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

7

22

×r

2

×(100)=1.54×1000

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

2

=

22×100

1.54×1000×7

\longrightarrow \sf{{r}^{2}= 49}⟶r

2

=49

\longrightarrow \sf{r = \sqrt{49}}⟶r=

49

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

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

2πr(r+h)

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

7

22

(7+100)

\longrightarrow \sf{=44\times107}⟶=44×107

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

2

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

2

=?m2:4708cm

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

100×100

4708

m

2

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

2

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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