Question

4. The capacity of a closed cylindrical vessel of height 1 m is 15-4 litres. How many square meter of metal sheet would be needed to make it​

Answer 1

Step-by-step explanation:

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Answer 2

CORRECT QUESTION:

The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it ?

GIVEN:

• Capacity of a closed cylindrical vessel is 15.4 litres.
• Height(h) of the closed Cylindrical vessel is 1 m

TO FIND:

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

SOLUTION:

Let the radius of the closed Cylindrical vessel be 'r' m.

• Capacity = 15.4 litre
• Height = 1 m

【$\bf{\star \: 1\: m^3 = 1000\: litres\: \star}$ 】

【 $\bf{\star\: \frac{1}{1000} m^3 = 1 \: litre\: \star}$ 】

【 $\bf{\star \: 1 \: litre = \frac{1}{1000} m^3\: \star}$ 】

Capacity = 15.4 litres = $\bf{\frac{15.4}{1000} \: m^3}$

Capacity = 0.0154 m³

We know that, the formula for finding the volume of cylinder is:-

$\bf{\star \: Volume\: of \: Cylinder = \pi r^2 h\: \star}$

According to question:-

On putting the given values in the formula, we get

Take π = 22/7

$\sf{\rightharpoonup 0.0154 = \frac{22}{7} \times r^2 \times 1}$

$\sf{\rightharpoonup 0.0154 \times 7 = 22 \times r^2 \times 1}$

$\sf{\rightharpoonup 0.1078 = 22 \times r^2 }$

$\sf{\rightharpoonup = r^2 = \cancel\dfrac{0.1078}{22}}$

$\sf{\rightharpoonup r^2 = 0.0049 }$

$\sf{\rightharpoonup r = \sqrt{0.0049}}$

$\bf{\rightharpoonup \: \star\: r = 0.07 \: m \: \star }$

❝ Radius of the closed Cylindrical vessel is 0.07 m ❞

Now, we have to find the area would be covered by the metal sheets

⚫ Area would be covered by metal sheets = 2πrh + πr² + πr²

Put the values in the formula:

Take π = 22/7

$\sf{\rightharpoonup Area = 2 \pi r h + 2\pi r^2}$

$\sf{\rightharpoonup Area = 2 \pi r(h + r)}$

$\sf{\rightharpoonup Area = 2 \times \frac{22}{7} \times 0.07(1 + 0.07)}$

$\sf{\rightharpoonup Area = 2 \times \frac{22}{\cancel{7}} \times \cancel{0.07} \times 1.07}$

$\sf{\rightharpoonup Area = 44 \times 0.01 \times 1.07}$

$\bf{\rightharpoonup \: \star \: Area = 0.4708 \: m^2 \: \star }$

❝ Hence, the area would be covered by metal sheet is 0.4708 m² ❞

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