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?

Answer 1

Hint: Use the following formulas to calculate capacity and area of the cylinder. Sheet required to make the cylinder is equal to that of the area of the cylinder.
Capacity = volume of cylinder = $ \pi {r^2}h $
Total Surface area (TSA) of cylinder = $ 2\pi r(r + h) $
 $ 1{m^3} = 1000l $ can be used to carry out required conversion.

Complete step-by-step answer:

Given: Height (h)= 1 m
Capacity = 15.4 l
To find: total surface area of the cylinder so as to know the amount of sheet to be used.
Converting volume in m3 (as area to be measured in m2)
Volume of the cylinder= 15.4 l
 $ = 15.4 \times (1/1000) $ $m^3$

We\[\] Know,
Volume of cylinder = $ \pi {r^2}h $
therefore, $ \pi {r^2}h = 154/10000 $
Substituting we get, $ $
\[22/7{\text{ }} \times {\text{ }}{r^2} \times 1 = 154/10000\]
Calculating for r:
\[{r^2} = (154/10000)(7/22)\]
Square rooting both sides:

\[\sqrt {{r^2}} = \sqrt {(7/100) \times (7/1} 00)\]
\[r = 7/100\]
\[r = 0.07\]m

Therefore the radius of the cylinder is 0.07.
For Finding the sheet required per meter square, we need to calculate the total surface area of the cylinder.
the metal sheet required to make this cylinder will be equal to Total Surface area (TSA) of cylinder = $ 2\pi r(r + h) $ [By substituting the value of r and h]
 $
   = 2 \times 22 \times (1/100)(7/100 + 1) \\
   = 44 \times 1/100 \times 107/100 \\
   = 0.4708 \\
  $
Therefore, the metal sheet required to make this cylinder is 0.4708 $m^2$.

Note: Always proceed with the question when the units are similar or else convert it.Provide the final answer with units as without it, the answer is considered to be incomplete.