) 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
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
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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