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Ex.13.6 Q6 Surface Areas and Volumes Solution - NCERT Maths Class 9

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Question

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

 Video Solution
Surface-Areas-And-Volumes
Ex exercise-13-6 | Question 6

Text Solution

Reasoning:

Surface area total of a closed cylinder is \(2\pi rh + 2\pi {r^2} \).

\(2\pi rh \) corresponds to the Curved Surface Area of the cylinder and  \(2\pi {r^2} \) corresponds to the area of the circular lids of the cylindrical vessel in order to make it a closed container. Volume of cylinder \(\pi {r^2}h \).

What is known?

Capacity and height of the cylinder.

What is unknown?

Metal sheet needed to make it.

Steps:

\(\begin{align}\text{Capacity} &= \rm{15.4 \, liters}\\ V &= \frac{{15.4}}{{1000}} = .0154\,\,\rm {m^3} \end{align}\)

\(\begin{align}\rm{Volume} &= \pi {r^2}h\\ 0.0154 &= \frac{{22}}{7} \times {r^2} \times 1 \\{r^2} &= \frac{{.0154 \times 7}}{{22}}\\{r^2} &= .0049\\r &= \sqrt {.0049} \\ &= 0.07\,\, \rm m \end{align}\)

Curved surface area

\[\begin{align} & = 2\pi rh + 2\pi {r^2} \\ & = 2\pi r(r + h) \\ & = 2 \times \frac{{22}}{7} \times 0.07 \times (0.07 + 1) \\ & = 0.4708\,\, \rm {m^2} \end{align}\]

Answer:

\(0.47\, \rm {m^2} \) of metal sheet would be needed.

  
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