there is a circular pound and footpath runs along its boundary .a man walks around exactly once keeping close to its edge .if his step is 44cm long he takes exactly 600 step to go around the pound .what is the radius of the pound.
Remember that the circumference is
c = 2πr
You can find c, and thus get r.
mkc
To find the radius of the pond, we can apply the formula for the circumference of a circle. The formula for the circumference is C = 2πr, where C is the circumference and r is the radius.
Given that the man takes 600 steps to go around the pond, and each step is 44 cm long, we can calculate the total distance covered by the man as follows:
Total distance = Number of steps * Length of each step
Total distance = 600 steps * 44 cm = 26,400 cm
We know that the total distance covered is equal to the circumference of the pond. So, we can set up the equation:
C = 26,400 cm
Since we are looking for the radius, we can rearrange the formula for the circumference to solve for the radius:
C = 2πr
Divide both sides by 2π:
r = C / (2π)
Substituting the value of C into the equation, we get:
r = 26,400 cm / (2π)
Using the approximate value of π = 3.14, we can calculate the radius:
r = 26,400 cm / (2 * 3.14)
r = 26,400 cm / 6.28
Calculating this value, we find:
r ≈ 4,203.18 cm
Therefore, the radius of the pond is approximately 4,203.18 cm.