Question

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

Answer 1

Hii friend,

HEIGHT OF CYLINDER = 1m

VOLUME OF CYLINDER = 15.4 L = 15400 m³

π²h = 15400

22/7× r² × 1 = 15400

r² = 4900

r = ✓4900 = 70

METALLIC SHEET USED FOR MAKING THE CYLINDER = CSA OF CYLINDER + AREA OF BOTTOM = 2πrh + πr² = πr(2h+r) = 22/7×70(2×1+70) = 220×72 = 15840 M²

HOPE IT WILL HELP YOU.... :-)

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

${\boxed{\sf\:{Radius\;of\;Cylinderical\;vessel=r}}}$

Height (h)

= 1m

$\textbf{\underline{Convert\;it\;into\;cm}}$

[1m = 100 cm]

= 100 cm

Also,

Volume = 15.4 litre

Convert it into cm³

= 15.4 × 10³ cm³

Now,

Volume of Cylinder = πr²h

$\tt{\rightarrow 15.4\times 10^3=\dfrac{22}{7}\times r^2\times 100}$

$\tt{\rightarrow r^2=\dfrac{15.4\times 10^3\times 7}{22\times 10^2}}$

$\tt{\rightarrow\dfrac{15.4\times 10\times 7}{22}}$

$\tt{\rightarrow\dfrac{154\times 7}{22}}$

= 7 × 7

= 7²

${\boxed{\sf\:{Area\;of\;sheet\;required}}}$

= CSA of Cylinder + Area of both circular end

= 2πrh + 2πr²

= 2πr(h + r)

$\tt{\rightarrow 2\times\dfrac{22}{7}\times 7(100+7)}$

= 44 × 107

= 4708 cm²

Convert it into m²

$\tt{\rightarrow\dfrac{4708}{100\times 100m^2}}$

= 0.4708 m²