A pond 100 feet in diameter is surrounded by a circular grass walk which is 2 feet wide .The number of square feet of grass on the walk is
a. 4 pi
b. 20 pi
c. 196 pi
d. 204pi
e. 270 pi
please answer and explain
figure the area of the pond
Add 2 to the radius and figure the new area
subtract the smaller from the larger.
smaller area
a=pi r^2
= pi 50^2
= 2500 pi
larger area
a=pi r^2
=pi 52 ^2
=2704 pi
2704-2500
=204
answer d
thank you
To find the number of square feet of grass on the walk surrounding the pond, we can calculate the area of the outer circle and subtract the area of the pond.
First, let's calculate the radius of the pond using the diameter given. The formula to calculate the radius is:
Radius = Diameter / 2
In this case, the diameter is 100 feet, so the radius would be:
Radius = 100 / 2 = 50 feet
Now, let's calculate the area of the outer circle which includes the grass walk. The formula to calculate the area of a circle is:
Area = π * Radius^2
Substitute the radius value into the formula to get:
Area of outer circle = π * 50^2
Area of outer circle = π * 2500
Area of outer circle = 2500π square feet
Next, we need to calculate the area of the pond. Since the pond has a diameter of 100 feet, the radius would be half of that:
Radius of pond = 100 / 2 = 50 feet
The formula for the area of a circle is the same as before:
Area = π * Radius^2
Substitute the radius value to find the area of the pond:
Area of pond = π * 50^2
Area of pond = π * 2500
Area of pond = 2500π square feet
Finally, to find the area of grass on the walk, we subtract the area of the pond from the area of the outer circle:
Area of grass walk = Area of outer circle - Area of pond
Area of grass walk = 2500π - 2500π
Area of grass walk = 0π = 0 square feet
Therefore, there is no grass on the walk surrounding the pond, so the answer is (a) 4π. However, since there is no option for 4π in the provided choices, the most accurate answer would be none of the above.