Question

The length of a cylindrical roller is 2 metre the diameter of its and is 1.4 metre find the area covered by ruler in 5 rotations

Answer 1

Answer :-

$\: \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of CSA of cylinder has been used. This is because while roling, only the curved surface of cylinder is used. Also, the bases are neglected because they have no role here. So, 1 time the CSA is the area covered by roller in one rotation. Then, we can multiply the number of rotations into the CSA.

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★ Formula Used :-

$\: \large{\boxed{\boxed{\sf{CSA \: of \: Cylinder \: = \: 2 \: \times \: \pi rh}}}}$

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★ Question :-

The length of a cylindrical roller is 2 metre the diameter of its and is 1.4 metre find the area covered by ruler in 5 rotations.

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★ Solution :-

Given,

» Length of the cylinder = h = 2 m

» Diameter of the cylinder = d = 1.4 m

» Radius of cylinder = r = ½ × d = ½ × 1.4 m

» Number of rotations done by Roller = 5

Then, according to the question :-

➺ CSA of Cylinder = 2πrh

$\: \\ \qquad \large{\bf{\longmapsto \: \: CSA \: of \: Cylinder \: = \: 2 \: \times \: \dfrac{22}{7} \: \times \: \dfrac{1.4}{2} \: \times \: \: 2 }}$

➺ CSA of Cylinder = 2 × 22 × 0.1 m × 2 m

➺ CSA of Cylinder = 8.8 m²

$\: \\ \qquad \qquad \large{\boxed{\tt{CSA \: of \: Roller \: = \: 8.8 \: m^{2}}}}$

Now area covered by roller is given as :-

➣ Area covered by roller = 5 × 8.8 m²

➣ Area covered by roller = 44 m²

$\: \large{\boxed{\rm{\leadsto \: Hence, \: the \: total \: area \: covered \: by \: the \: roller \: is \: \boxed{\underline{44 \: m^{2}}}}}}$

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$\: \: \boxed{\boxed{\rm{\mapsto \: \: Reference \: as \: Supplementary \: Counsel \: }}}$

• CSA of Cube = 4 × Side²

• CSA of Cone = πrl

where l is the slant height.

• TSA of Cube = 6 × Side²

• Volume of Cube = Side³

• Volume of Cuboid = Length × Breadth × Height

• Volume of Cone = ⅓ × πr²h

• Volume of Cylinder = πr²h

Answer 2

Given :

The length of a cylindrical roller is 2 metre the diameter of its is 1.4 metre

To find :

The area covered by ruler in 5 rotations .

Solution :

Here we have :

⇒ Height of cylindrical roller (h) = 2 m

⇒ Diameter of roller = 1.4 m

∴ Radius of roller (r) = 1.4/2 m

∴ Radius of roller (r) = 0.7 m

Now we know,

CSA of cylinder = 2πrh

⇒ CSA of cylindrical roller = 2 * 22/7 * 0.7 * 2

⇒ CSA of cylindrical roller = 61.6/7

⇒ CSA of cylindrical roller = 8.8 m²

Now we know that,

Area covered = CSA of roller * Number of rotations

⇒ Area covered = 8.8 * 5

⇒ Area covered = 44 m²

Therefore,

Area covered by roller in 5 rotations = 44 m²