Math, asked by Gangotri7929, 5 months ago

) You are going to play a cricket match in a stadium having a circular field of circumference
100 m. A pitch of width 5 m has been carved outside the circular field.
What is the ratio of the area of the pitch to the area of the circular field?

Answers

Answered by Brilliantguy23
8

Step-by-step explanation:

Circumference of the field = 100 m

ie, 2πr = 100πr = 50r = 50 / π = (50×7)22m

Area of the field = πr² = 22/7×

(50×7)/22

Area = 50 m²Length of pitch = diameter of field = 2×(50×7)/22 = 31.81 m

Width = 5 m

Area of pitch = 31.81 × 5 = 159.05 m²

Area of field : Area of pitch = 50 : 159.05 = 1 : 3.181

Is this the answer

Answered by amitnrw
1

Given : a stadium having a circular field of circumference  100 m

A pitch of width 5 m has been carved outside the circular field.

To Find  : ratio of the area of the pitch to the area of the circular field?

Solution:

stadium having a circular field of circumference  100 m.

circumference = 2πr

=> 2πr =  100

=> r = 50/π

Radius of ground = 50/π  m

Area of ground = π (50/π)²  = 2500/π  m²

pitch of width 5 m has been carved outside the circular field.

Area of pitch =   π( 50/π + 5)²  - π (50/π)²

= π( 50/π + 5 + 50/π)( 50/π + 5 - 50/π)

= π( 100/π + 5)( 5)

= 500 + 25π

ratio of the area of the pitch to the area of the circular field

= (500 + 25π)/(2500/π)

=(500π + 25π²)/2500

= (20π + π²)/100

= π(20 + π)/100

= 0.727

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