Question

A garden roller of diameter 1 m is 2.1 m long. Find the area it covers in 100
revolutions.​

Answer 1

Given :-

Diameter of the garden roller = 1 m

Length of the garden roller = 2.1 m

To Find :-

The area covered in 100 revolution.

Analysis :-

Firstly, find the curved surface area of the roller of height given.

Multiply the number we got by 100 in order to find the area covered in 100 revolution.

Solution :-

We know that,

• r = Radius
• d = Diameter
• h = Height

Using the formula,

$\underline{\boxed{\sf Surface \ area \ of \ a \ cylinder=2 \pi rh}}$

Given that,

Radius (r) = d/2 = 1/2 = 0.5 m

Height (h) = 2.1 m

Substituting their values,

⇒ 2 × (22/7) × 1/2 × 2.1

⇒ 66/10

⇒ 6.6 m²

According to the question,

Area covered in 100 revolution = 100 × Curved surface area

Substituting their values,

⇒ 100 × 6.6

⇒ 660 m²

Therefore, the area it covers in 100  revolutions is 660 m².

Answer 2

Answer:

$\huge \fbox {given}$

$\sf \implies \: diameter \: of \: garden \: roller \: = 1 m$

$\sf \implies \: length \: of \: roller \: = 2.1 \: m$

$\huge \fbox {to \: find}$

$\sf \implies \: area \: cover \: in \: 100 \: revolution$

$\huge \fbox {solution}$

First we have to find area of 1 revolution

$\huge \bf \: area \: = 2\pi \: rh$

$\sf \implies \: height \: = 1m \: = 100 \: cm$

$\: \sf \: long\: 2.1 \: m \: = 2 \times 100 + 10 = 210 \: cm$

$\sf \implies \: 2 \times \frac{22}{7} \times 100 \: cm \: \times 210 \: cm$

$\sf 2 \times 22 \times 100 \times 30$

$\huge \bf \: 132000 \: cm \: or \: 132 \: m$

Area of 100 revolution = 132000 × 100 = 13200000 cm