in a circular park with a radius of 250 m there are 7 lamps whose bases are circles with a radius of 1m. The entire area of the park has grass with the exception of the bases of the lamps. Calculate the lawn area.
To calculate the lawn area, we need to find the total area of the circular park and subtract the sum of the areas of the bases of the lamps.
The total area of the circular park is given by the formula: A = πr^2
Where A is the area and r is the radius.
So, the total area of the park
= π(250m)^2
= 62500π m^2
The area of one lamp base is given by the formula: A = πr^2
Substituting the given radius of 1m, we find:
The area of one lamp base = π(1m)^2
= π m^2
As there are 7 lamps, the total area of the bases of the lamps is:
7 * π m^2
Finally, to find the lawn area, we subtract the area of the bases of the lamps from the total area of the park:
Lawn area = total area of the park - area of bases of the lamps
= 62500π m^2 - 7π m^2
= (62500 - 7)π m^2
= 62493π m^2
Therefore, the lawn area is approximately 62493π square meters.