need help with word problem
The Parks Department is planting a circular garden in the city park. The diameter of the garden is 10 feet. The concrete mowing strip is around the garden is one foot wide. What is the area of the mowing strip?
A= 3.14 x 6 square -radius is 6,half of diameter of 12
Is the correct set-up?
Ag + As = At
As = At - Ag
As = 3.14*6^2 - 3.14*5^2 = Area of strip.
At = Total area.
Ag = Area of garden.
Yes, your set-up is almost correct. To find the area of the mowing strip, you need to subtract the area of the circular garden from the area of the larger circle formed by the outer edge of the mowing strip.
To find the area of the circular garden, you use the formula A = πr², where r is the radius of the garden. Given that the diameter is 10 feet, the radius is half of that, which is 10 / 2 = 5 feet. Therefore, the area of the garden is A = π(5)² = 25π square feet.
To find the area of the larger circle formed by the outer edge of the mowing strip, you need to add the width of the mowing strip (1 foot) to the radius of the garden. So, the radius of the larger circle is 5 + 1 = 6 feet.
Now, you can use the same formula A = πr² to find the area of the larger circle. Plugging in the radius of 6 feet, the area is A = π(6)² = 36π square feet.
To find the area of the mowing strip, subtract the area of the garden from the area of the larger circle:
Area of mowing strip = Area of larger circle - Area of garden
Area of mowing strip = 36π - 25π = 11π square feet.
The correct set-up is: the area of the mowing strip is equal to 11π square feet.