Question

Find the area covered bya roller of diameter 2.1 m and lenghth 4m in one revolution

Answer 1

Answer:

26.4 m²

Step-by-step explanation:

As per the provided information in the given question, we have :

• Diameter of the roller = 2.1 m
• Length of the roller = 4 m

We have been asked to calculate the area covered by a roller in one revolution.

The roller exists in cylindrical shape. So, the area covered by a roller in one revolution will be equal to the lateral surface area of the roller.

→ Lateral surface area of roller = Lateral surface area of cylinder

★ Lateral Surface Area of Cylinder = 2πrh

• π = 22/7
• r denotes radius
• h denotes height [length]

Let's find out radius first.

↠ Diameter = 2 × Radius

↠ Radius = Diameter ÷ 2

↠ Radius = 2.1 m ÷ 2 [Since, diameter = 2.1 m]

↠ Radius = 1.05 m

Now, substitute all the values in the formula of lateral surface area of cylinder.

→ Lateral Surface Area of roller = 2πrh

→ Lateral Surface Area of roller = 2 × (22/7) × 1.05 × 4 m²

→ Lateral Surface Area of roller = 2 × 22 × 0.15 × 4 m²

→ Lateral Surface Area of roller = 44 × 0.15 × 4 m²

→ Lateral Surface Area of roller = 26.4 m²

Therefore, the area covered by a roller in one revolution is 26.4 m².

$\rule{200}2$

Answer 2

Answer:

Given :-

• A roller of diameter 2.1 m and length is 4 m in one revolution.

To Find :-

• What is the area covered by a roller.

Formula Used :-

$\clubsuit$ Radius Formula :

$\longrightarrow \sf\boxed{\bold{\pink{Radius =\: \dfrac{Diameter}{2}}}}$

$\clubsuit$ Curved Surface Area or C.S.A of Cylinder Formula :

$\longrightarrow \sf\boxed{\bold{\pink{Curved\: Surface\: Area_{(Cylinder)} =\: 2{\pi}rh}}}$

where,

• π = Pie or 22/7
• r = Radius
• h = Height

Solution :-

First, we have to find the radius :-

$\implies \sf Radius =\: \dfrac{2.1}{2}$

$\implies \sf\bold{\purple{Radius =\: 1.05\: m}}$

Hence, the radius is 1.05 m .

Now, we have to find the area covered by a roller :

Given :

• Pie (π) = 22/7
• Radius (r) = 1.05 m
• Height (h) = 4 m

According to the question by using the formula we get,

$\dashrightarrow \bf C.S.A_{(Roller)} =\: 2{\pi}rh$

$\dashrightarrow \sf C.S.A_{(Roller)} =\: 2 \times \dfrac{22}{7} \times 1.05 \times 4$

$\dashrightarrow \sf C.S.A_{(Roller)} =\: \dfrac{44}{7} \times 4.2$

$\dashrightarrow \sf C.S.A_{(Roller)} =\: \dfrac{44 \times 4.2}{7}$

$\dashrightarrow \sf C.S.A_{(Roller)} =\: \dfrac{184.8}{7}$

$\dashrightarrow \sf\bold{\red{C.S.A_{(Roller)} =\: 26.4\: m^2}}$

$\therefore$ The area covered by a roller is 26.4 m².

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