which has a greater area, a circular garden with a diameter of 20 meters or a square garden with sides with sides that are 20 meters long
A square garden
Circular Garden Area= pi r squared=314 meters
Square Garden=Length*Width=400 meters
Circle:
A = pi * r^2
A = 3.14 * 10^2
A = 3.14 * 100
A = ?
Square:
A = s^2
A = 20 * 20
A = ?
To determine which garden has a greater area, we can calculate the area of each shape.
The area of a circular garden can be calculated using the formula:
Area = π * radius^2
Given that the diameter of the circular garden is 20 meters, we can find the radius by dividing the diameter by 2:
Radius = Diameter / 2 = 20 m / 2 = 10 m
Using this value, we can calculate the area of the circular garden:
Area (circular garden) = π * 10 m^2
The area of a square garden can be calculated using the formula:
Area = side length^2
Given that the side length of the square garden is 20 meters, we can calculate its area:
Area (square garden) = 20 m * 20 m
Now let's compare the areas:
Area (circular garden) = π * 10^2 m^2
Area (circular garden) = π * 100 m^2
Area (square garden) = 20 m * 20 m
Area (square garden) = 400 m^2
Comparing the two areas, we can see that the area of the square garden (400 m^2) is greater than the area of the circular garden (π * 100 m^2). So, the square garden has a larger area than the circular garden.
To determine which garden has a greater area, we need to compare the areas of the circular garden and the square garden.
To find the area of the circular garden, we need to use the formula for the area of a circle, which is:
Area = π * radius^2
Given that the diameter of the circular garden is 20 meters, we can find the radius by dividing the diameter by 2:
Radius = Diameter / 2 = 20 / 2 = 10 meters
Now, we can calculate the area of the circular garden using the formula:
Area of circular garden = π * (radius)^2 = π * 10^2 = 100π square meters
To find the area of the square garden, we need to use the formula for the area of a square, which is:
Area = side^2
Given that the sides of the square garden are 20 meters long, we can calculate the area:
Area of square garden = (side)^2 = 20^2 = 400 square meters
Comparing the areas of the circular garden and the square garden, we have:
Area of circular garden = 100π square meters
Area of square garden = 400 square meters
Now, we need to compare these values. However, we need to know the approximate value of π (pi). π is an irrational number with an approximate value of 3.14159. Let's substitute this value into the calculation:
Area of circular garden ≈ 100 * 3.14159 ≈ 314.16 square meters
Comparing the values of the areas, we see that the square garden has a greater area of 400 square meters compared to the circular garden's approximate area of 314.16 square meters. Therefore, the square garden has a greater area.