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A roll of newspaper of length $7000{\text{ m}}$ and thickness $0.022{\text{ cm}}$ is rolled into a solid cylinder Find its radius.
(A) $7{\text{ cm}}$
(B) $140{\text{ cm}}$
(C) $35{\text{ cm}}$
(D) $70{\text{ cm}}$

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Last updated date: 17th Jun 2024
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Answer
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Hint: We have given the length and thickness of the newspaper this means the newspaper is in the shop of cuboid length and thickness have difficult units so we have to change in the same unit. We consider the height of a newspaper is equal to $h$. As the newspaper is rolled in the form of a cylinder in height the cylinder will be equal to bread of newspaper. Also the volume of the newspaper will be equal to the volume of the cylinder. We equal volume of both can find the radius.

Complete step-by-step answer:
We have given that the length of roll of newspaper is $7000$ and thickness is $0.022{\text{ cm}}$
It is rolled in the form of a solid cylinder. Newspapers are in the shape of a cuboid. So lengths of
$ \Rightarrow$ ${\text{cuboid (}}l{\text{) = }}7000m$
$ \Rightarrow$ $1m = 100cm$
So $7000m = 7000 \times 100cm$
Length of ${\text{cuboid (}}l{\text{) = }}700000cm$
Thickness of ${\text{cuboid (}}h{\text{) = }}0.022cm$
Let Breadth of cuboid $ = $ \[b\]
The newspaper is rolled in the shape of a cylinder. Therefore, the volume of the cylinder will be equal to the volume of the cuboid.
 Also height of cylinder $ \Rightarrow $ Breadth of cuboid$ = $ b
Let $'r'$ be the radius of cylinder
Volume of cylinder = volume of cuboid
$ \Rightarrow$$\pi {r^2}b = l \times h \times b$
$ \Rightarrow$$\pi {r^2} = l \times h$
Value of $\pi $ is equal to $\dfrac{{22}}{7}$
$ \Rightarrow$$\dfrac{{22}}{7} \times {r^2} = 700000 \times 0.022$
$ \Rightarrow$${r^2} = \dfrac{{700000 \times 22 \times 7}}{{22 \times 1000}}$
$ \Rightarrow$${r^2} = 700 \times 7$
$ \Rightarrow$${r^2} = 4900$
Taking square root on both sides
$ \Rightarrow$$r = \sqrt {4900} {\text{ }} \Rightarrow 70$
$ \Rightarrow$$r = 70cm$
Radius of cylinder $ = 70{\text{ cm}}$

Option (D) is correct.


Note: Volume is the quantity of three dimensional space enclosed by a closed surface. For example, the space that a substance or shape occupies OC contains. Volume often qualified by numerically using the SI derived unit cubic meter. Right circular cylinder is a three dimensional figure in which there are two flat ends in the shape of circles. These two faces are connected by a curved face that looks like a tube. If you make a flat net for a cylinder, it looks like a rectangle with a circle attached at each end.