Name: Surface Area: Cube, Cuboid and Cylinder
Uploaded: 2019-07-19
Duration: 11 min 14 s
Description: This video explains what surface and surface area are. It also describes the surface area of cubes, cuboids and cylinders with different examples. Learn more in this video.

Question

A rectangular sheet of paper

35 cm \times 21 cm

can be transformed into the curved surface of a right circular cylinder in two ways, i.e., either by rolling the paper along its length or along its breadth. Find the ratio of the volumes of the two cylinders thus formed.

Accepted Answer

Dimensions of the rectangular sheet of paper $= 35 cm \times 21 cm$

We have to find the ratio of the volumes of the cylinders formed by rolling the sheet along its length and along its breadth.

Let $V_{1}$ be the volume of the cylinder which is formed by rolling the sheet along its length.

When the sheet is rolled along its length, the length of the sheet forms the perimeter of the base of the cylinder. Therefore, we have,

$2 π r_{1} = 35$

$r_{1} = \frac{35}{2 π}$

The width of the sheet will be equal to the height of the cylinder. Therefore,

$h_{1} = 21 cm$

Therefore,

$V_{1} = π r_{1}^{2} h_{1}$

$= π \times \frac{35}{2 π} \times \frac{35}{2 π} \times 21$

$V_{1} = \frac{35 \times 35}{4 π} \times 21 {cm}^{3}$ .

Let $V_{2}$ be the volume of the cylinder formed by rolling the sheet along its width.

When the sheet is rolled along its width, the width of the sheet forms the perimeter of the base of the cylinder. Therefore, we have,

$2 π r_{2} = 21$

$r_{2} = \frac{21}{2 π}$

The length of the sheet will be equal to the height of the cylinder. Therefore,

$h_{2} = 35 cm$

Now,

$V_{2} = π r_{2}^{2} h_{2}$

$= π \times \frac{21}{2 π} \times \frac{21}{2 π} \times 35$

$V_{2} = \frac{21 \times 21}{4 π} \times 35 {cm}^{3}$

Now that we have the volumes of the two cylinders, we have,

$\frac{V_{1}}{V_{2}} = \frac{\frac{35 \times 35}{4 π} \times 21}{\frac{21 \times 21}{4 π} \times 35}$

$\frac{V_{1}}{V_{2}} = \frac{35}{21} = \frac{5}{3}$

Therefore, the ratio of the volumes of the two cylinders is $5 : 3$ .

A rectangular sheet of paper $35 cm \times 21 cm$ can be transformed into the curved surface of a right circular cylinder in two ways, i.e., either by rolling the paper along its length or along its breadth. Find the ratio of the volumes of the two cylinders thus formed.

Important Questions on Mensuration-II (Solid Figures)

Learn and Prepare for any exam you want !

A rectangular sheet of paper 35 cm×21 cm can be transformed into the curved surface of a right circular cylinder in two ways, i.e., either by rolling the paper along its length or along its breadth. Find the ratio of the volumes of the two cylinders thus formed.

Important Questions on Mensuration-II (Solid Figures)

Learn and Prepare for any exam you want !

A rectangular sheet of paper $35 cm \times 21 cm$ can be transformed into the curved surface of a right circular cylinder in two ways, i.e., either by rolling the paper along its length or along its breadth. Find the ratio of the volumes of the two cylinders thus formed.