Question

To cover a distance of 10 km a wheel rotates 5000 times. Find the radius of the wheel.

Answer 1

Answer:

I hope it helps you.

Step-by-step explanation:

No. of rotations = 5000.

Total distance covered = 10 km, and we have to find out the radius of the circle.

Let ‘r’ be the radius of the wheel

Circumference of the wheel = Distance covered in 1 rotation = 2πr.

In 5000 rotations, the distance covered = 10 km = 1000000 cm.

Hence, in 1 rotation, the distance covered = 10000005000cm=200cm

But this is equal to the circumference. Hence, 2πr = 200 cm

r = 200/2π

r = 100/π

Taking the approximate value of π as 22/7, we get

r = 100 x 7/22

r = 31.82 cm approx.

Answer 2

Answer:

The radius of the wheel =31.82cm

Step-by-step explanation:

Given,

No. of rotations made by the wheel to cover a distance of 10km = 5000

To find,

The radius of the wheel

Recall the formula,

The circumference of a circle = 2πr, where 'r' is the radius of the circle.

Solution

Distance covered when the wheel rotates once  = Circumference of the wheel.

Distance traveled by the wheel to make 5000 rotations = 10km

Distance traveled by the wheel to make 1 rotation = $\frac{10}{5000}$km = $\frac{10000}{5000}$m= 2m(∵1km = 1000m)

∴Circumference of the wheel = 2m

2πr = 2

r =$\frac{1}{\pi }$m

r = $\frac{7}{22}$ m = $\frac{700}{22} cm$ = 31.82cm

∴The radius of the wheel =31.82cm

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