Question

A closed cylindrical tank of radius 14 m and height 6 m is made from a sheet of metal. How much sheet of metal is required

Answer 1

radius = 14m
height = 6m
total surface area of a cylinder =
2 × pi × r × (r + l)
= 2 × 22/7 × 14 × {14 + 6}
= 2×22×2×20
=1760

Answer 2

1760 m² sheet of metal is required.

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Let's understand a few concepts:

While calculating the area of a closed cylinder the area of the top and bottom part of the cylinder is also considered along with its curved surface area.

Therefore, the surface area of a closed cylinder is as follows:

$\boxed{\bold{Total \:surface\:area\:of\:closed\:cylinder = \pi r^2 + 2\pi rh + \pi r^2 = 2\pi r^2 + 2\pi rh = 2\pi r (r+h)}}$

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Let's solve the given problem:

The radius of the closed cylinder (r) = 14 m

The height of the closed cylinder (h) = 6 m

Therefore,

The required area of the sheet of metal to make the closed cylinder is,

= Total surface area of a closed cylinder

= $2\pi r (h + r)$

= $2\times \frac{22}{7} \times 14 \times (6 + 14)$

= $2\times \frac{22}{7} \times 14 \times 20$

= $2\times 22 \times 2 \times 20$

= $\bold{1760\:m^2}$

Thus, a 1760 m² sheet of metal is required to make a closed cylinder of radius 14 m and height 6 m.

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