Question

Find the number of revolutions made by a circular wheel of area 1.54 m2

Answer 1

Area of the circle= 1.54 m²
=> πr²= 1.54 m²
=> 22/7×r²= 1.54m
=> r²= 1.54×7/22
=> r²= 0.49
=> r= √0.49
=> r= 0.7m

Circumference of the wheel= 2πr
=2×22/7×0.7m
=2×22×0.1m
=44×0.1m
=0.44m

Revolution of the wheel = distance/circumference
=distance/0.44

Answer 2

Let the radius = r

Given Area = 1.54 m².

Then ,

πr² = 1.54

$\frac{22}{7} \times {r}^{2} = 1.54 \\ \\ {r}^{2} = 7 \times 0.07 \\ \\ = 0.49 \\ \\ r = 0.7 \: m$

The required radius = 0.7 m

Then ,

Let's suppose the number of revolutions made by wheel = n

Then ,

n × Distance rolled in one revolution = 176

[Distance revolved in one revolution = It's circumference]

n × 2πr = 176

$n \times 2 \times \frac{22}{7} \times 0.7 = 176 \\ \\ n = \frac{176 \times 7}{2 \times 22 \times 0.7} = 40$

The number of revolutions required = 40.