Question

The capacity of a closed cylindrical vessel of height 1m is 15.4 litres. How many square metres of metal sheet would be needed to make it ? [Assume π = 22/7]

Answer 1

Question :–

The capacity of a closed cylindrical vessel of height 1m is 15.4 litres. How many square metres of metal sheet would be needed to make it ? [Assume π = $\sf \frac{22}{7}$ ]

Given :–

• h = 1m = 100cm.
• Capacity = 15.4 litres.

To Find :–

• How many square metres of metal sheet would be needed to make it ?

Solution :–

• h = 1m = 100cm
• Capacity = 15.4 litre

Volume = 15.4 × 1000 cm³ [1 lit. = 1000 cm³]

πr²h = 15400.0 cm³

$\sf \frac{22}{7}$ × r² × 100 = 15400

r² = $\sf \frac{ \cancel{154} \cancel{00} \times 7}{ \cancel{22} \times 1 \cancel{00}}$

r² = (7)²

r = 7cm

Required metal sheet :–

→ T.S.A. of cylinder.

→ 2πr(r + h)

→ 2 × $\sf \frac{22}{\cancel{7}}$ × $\cancel{7}$ (7 + 100)

→ 44 (107)

→ 4708 cm²

→ $\sf \frac{4708}{100 \times 100}$ m²

→ $\sf \frac{4,708}{10,000}$

→ 0.4708m²

Answer 2

Answer:

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

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

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

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

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