A circular garden of radius 25m has a concentric circular fountain of radius 3m.find the area of the garden available for the children to playin.
Radius of circular garden=25m
Radius of inner circle=25-3
=22m
Area of garden available to play children in=pie r^2
=3.14×(22)^2
=3.14×484
=1519.760m^2
you know how to find the area of a circle: A = πr^2
so, subtract the area of the small circle from that of the large one.
To find the area of the garden available for the children to play in, subtract the area of the fountain from the area of the garden.
1. Area of the garden:
The area of a circular garden can be found using the formula A = πr^2, where r is the radius.
The radius of the garden is 25m, so the area of the garden is: A_garden = π * 25^2
2. Area of the fountain:
The area of a circular fountain can also be found using the same formula. The radius of the fountain is 3m, so the area of the fountain is: A_fountain = π * 3^2
3. Area available for the children to play in:
To find this area, subtract the area of the fountain from the area of the garden.
A_available = A_garden - A_fountain
Plugging in the values from step 1 and step 2:
A_available = π * 25^2 - π * 3^2
Simplifying the expression:
A_available = π * (25^2 - 3^2)
Calculating the values inside the parentheses:
A_available = π * (625 - 9)
A_available = π * 616
Therefore, the area of the garden available for the children to play in is approximately 616π square meters.
To find the area of the garden available for the children to play in, we need to subtract the area of the fountain from the area of the entire circular garden.
The formula to find the area of a circle is given by A = πr², where A is the area and r is the radius.
Area of the garden = π(25m)² = π(625m²) = 625π m²
Area of the fountain = π(3m)² = π(9m²) = 9π m²
Therefore, the area of the garden available for the children to play in is:
625π m² - 9π m² = (625 - 9)π m² = 616π m²
So, the area of the garden available for the children to play in is 616π square meters.