Question

Lamar and Avalon are raking the leaves around a tree in their backyard. The has a diameter of 2 feet and is surrounded by a circle of leaves that is 24 feet in diameter. What is the area in square feet of the ground covered by leaves? Use 3.14 for

Answer 1

We have two cirlces:
big circle⇒ diameter=24 ft
small circle⇒diameter 2 ft

Area of the ground covered by leaves=area of the larger circle- area of the small circle.

1) we calculate the area of the larger circle
Data:
diameter=24 ft
radius=diameter / 2=24 ft /2=12 ft

Area of the larguer circle=πr²=π(12 ft)²=144π ft²

2)We calculate the area of the small circle
Data:
diameter=2 ft
radius=diameter/2=2 ft/2=1ft

Area of the small circle=πr²=π(1 ft)²=π ft²

3) we calculate the area of the ground covered by leaves.
area of the ground covered by leaves=144π ft²-π ft²=143π ft²≈143*(3.14) ft²=
=449.02 ft²

Answer: the area of the ground covered by leaves is 449.02 ft².

Answer 2

The area of a circle is determined by pir^2 (remember that the exponent belongs to the radius). We can use 3.14 for pi. So, the new expression would be 3.14*r^2.

I'm assuming that when you said "The has a diameter of 2 feet", you are talking about the tree. If that is the case, you need to subtract the area of the tree from the area of the pile of leaves. Let's begin by calculating the areas using 3.14*r^2.

Area of tree: 3.14 ft^2
3.14*r^2
We need to find the radius, not the diameter. The radius is half of the diameter so we can take half of the diameter, which is 2 feet, to get 1 feet.
3.14*1^2
3.14*1
3.14

Area of circle of leaves: 452.16 ft^2
3.14*r^2
Again, we need the radius, not the diameter. So, we can take half of the diameter, 24 feet, to get 12 feet.
3.14*12^2
3.14*144
452.16 feet

Now, we can subtract.

452.16-3.14=449.02 ft^2