Question

Arthur ran around a circular field three times if he ran a total distance of 660 M what is the diameter and radius of the field​

Answer 1

Given :

Arthur ran around a circular field three times if he ran a total distance of 660 m.

To Find :

The diameter and radius of the field.

Solution :

Analysis :

Here we first have to find the circumference by dividing the total distance by number of rounds. Then using that we can get the circumference and from that circumference we can get the radius by using the correct formula of circumference.

Required Formula :

• Circumference of Circle = 2πr

• Diameter = 2 × Radius

where,

• π = 22/7
• r = radius

Explanation :

It is said that Arthur ran around a circular field three times of a total distance of 660 m.

So,

The circumference = Total distance/3

= 660/3

= 220 m

∴ Circumference of circle = 220 m.

Let us assume that the radius is "r" m.

We know that if we are given the circumference of the circle and is asked to find the radius of the circle then our required formula is,

Circumference of Circle = 2πr

where,

• Circumference = 220 m
• π = 22/7
• r = r m

Using the required formula and substituting the required values,

⇒ Circumference of Circle = 2πr

⇒ 220 = 2 × 22/7 × r

⇒ 220 = 44/7 × r

⇒ 220 × 7/44 = r

⇒ 1540/44 = r

⇒ 35 = r

∴ Radius = 35 m.

Verification :

⇒ Circumference of Circle = 2πr

• Putting r = 35 m,

⇒ 220 = 2 × 22/7 × 35

⇒ 220 = 44/7 × 35

⇒ 220 = 1540/7

⇒ 220 = 220

∴ LHS = RHS.

• Hence verified.

Now the diameter :

We know that if we are given the radius and is asked to find the diameter then our required formula is,

Diameter = 2 × Radius

where,

• Radius = 35 m

Using the required formula and substituting the required values,

⇒ Diameter = 2 × Radius

⇒ Diameter = 2 × 35

⇒ Diameter = 70

∴ Diameter = 70 m.

Radius = 35 m.

Diameter = 70 m.