A person observed that he required 30 seconds less time to cross a circular ground along its diameter than to cover it once along the boundary. If his speed was 30 m/minute, then the radius of the circular ground is
Answers
Given:
30 second less to cross the via the diameter than the arc.
His speed is 30 metre/minute
To Find:
The length of the radius
Explanation:
When he walked along the boundary from the beginning of the diameter to the end of the diameter, he only needs to walk half the circle (which is semicircle).
Solution
Find the distance he can cover in 30 Seconds:
Speed = 30 m/min
1 minute = 30 metre
1 second = 30 ÷ 60
1 second = 0.5 metre
30 seconds = 0.5 x 30
30 seconds = 15 metres
Find the diameter in term of radius:
Diameter = 2 x Radius
Diameter = 2r
Find the circumference of the semi-circle:
Circumference of semicircle = 1/2 (2πr)
Circumference of semicircle = πr
Solve x:
πr - 2r = 15 metres
r(π - 2) = 15
r = 15 ÷ (π - 2)
r = 13.125 metres
Answer: The radius is 13.125 m