Mr. Petri has a rectangular plot of land with length=20 feet and width=10 feet. He wants to design a flower garden of o circle with two semicircles at each end of the center circle. he will fill in the shaded region with wood chips. if one bag of wood chips covers 5 square feet, how many bags must he buy?
How big are the circle and semicircles? If the diameter is 10 feet, you won't be able to walk around the center circle
To find out how many bags of wood chips Mr. Petri needs to buy, we need to calculate the area of the shaded region in the flower garden.
First, let's calculate the area of the rectangular plot:
Area of the rectangular plot = length * width
= 20 feet * 10 feet
= 200 square feet
Next, let's calculate the area of the center circle:
The radius of the circle is the width of the rectangular plot, which is 10 feet.
The formula for the area of a circle is A = π * r^2, where A is the area and r is the radius.
Area of the center circle = π * (radius)^2
= π * (10 feet)^2
= π * 100 square feet
Now, let's calculate the area of each semicircle (one at each end):
The radius of the semicircle is half the width of the rectangular plot, which is 10 feet / 2 = 5 feet.
Area of each semicircle = (1/2) * π * (radius)^2
= (1/2) * π * (5 feet)^2
= (1/2) * π * 25 square feet
= 12.5π square feet
The total area of the shaded region (center circle + 2 semicircles) is:
Total area = Area of the center circle + 2 * Area of each semicircle
= π * 100 square feet + 2 * 12.5π square feet
= 100π square feet + 25π square feet
= 125π square feet
Since one bag of wood chips covers 5 square feet, we can find the number of bags needed by dividing the area of the shaded region by 5:
Number of bags needed = Total area / Area covered by one bag
= 125π square feet / 5 square feet
= 25π bags
Therefore, Mr. Petri needs to buy approximately 25π (about 78.54) bags of wood chips to cover the shaded region in his flower garden.
To find out how many bags of wood chips Mr. Petri needs to buy, we first need to calculate the area of the shaded region.
1. Calculate the area of the rectangular plot of land:
The formula for the area of a rectangle is length × width.
Area = 20 feet × 10 feet = 200 square feet.
2. Calculate the area of the center circle:
The formula for the area of a circle is πr², where "r" is the radius of the circle.
Since the diameter of the circle is equal to the width of the rectangular plot, the radius will be half of that.
Radius = width/2 = 10 feet/2 = 5 feet.
Area of the circle = π × (5 feet)² = 25π square feet.
3. Calculate the area of two semicircles at each end of the center circle:
The formula for the area of a semicircle is ½(πr²), where "r" is the radius of the semicircle.
The diameter of each semicircle is equal to the length of the rectangular plot, so the radius will be half of that.
Radius = length/2 = 20 feet/2 = 10 feet.
Area of two semicircles = 2 × (½π × (10 feet)²) = 100π square feet.
4. Calculate the total area of the shaded region:
Total shaded area = Area of the rectangular plot - Area of the center circle - Area of two semicircles.
Total shaded area = 200 square feet - 25π square feet - 100π square feet.
Simplifying, Total shaded area = 200 square feet - 125π square feet.
5. Calculate the number of bags of wood chips needed:
If one bag of wood chips covers 5 square feet, we divide the total shaded area by 5.
Number of bags = Total shaded area / 5 = (200 square feet - 125π square feet) / 5.
Since we don't know the exact value of π, we can use an approximation, such as 3.14, to calculate the number of bags. Plugging in the values, we get:
Number of bags ≈ (200 square feet - 125 × 3.14 square feet) / 5
Simplifying further, we get:
Number of bags ≈ (200 square feet - 392.5 square feet) / 5
Number of bags ≈ -192.5 square feet / 5
Number of bags ≈ -38.5 bags
Since the number of bags cannot be negative, we round up to the nearest whole number.
Therefore, Mr. Petri needs to buy 39 bags of wood chips to cover the shaded region.