Marcy is making a hooked circle-shaped rug for her mother. The circumference of the circle-shaped rug is 62.8 inches.
What is the area of the rug? (Use 3.14 for pie .)
A.
31.4 in2
B.
214 in2
C.
314 in2
D.
628 in2
To find the area of the circle-shaped rug, we need to use the formula A = πr², where A is the area, π is 3.14, and r is the radius of the circle. We know that the circumference is 62.8 inches, which means that:
2πr = 62.8
Dividing both sides by 2π, we get:
r = 10
So the radius of the rug is 10 inches. Now we can plug this into the formula for area:
A = 3.14 x 10²
A = 314
Therefore, the area of the rug is 314 square inches, which is answer choice C.
On a circular playground, the distance from its center to the edge of the playground is 40 feet. What is the approximate circumference of the playground? (Use 3.14 for pie .)
A.
251.20 ft
B.
5,024.00 ft
C.
20,096.00 ft
D.
125.60 ft
The distance from the center of the circle to its edge is the radius of the circle. We know that the radius is 40 feet. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. Plugging in the values, we get:
C = 2 x 3.14 x 40
C = 251.2
Therefore, the approximate circumference of the playground is 251.2 feet, which is answer choice A.
To find the area of a circle, you need to square the radius and multiply it by pi (π).
The formula to find the circumference of a circle is: circumference = 2πr
Given that the circumference of the rug is 62.8 inches, we can calculate the radius using the formula:
circumference = 2πr
62.8 = 2 * 3.14 * r
r = 62.8 / (2 * 3.14)
r ≈ 10
Now that we have the radius, we can find the area of the rug using the formula:
area = πr^2
area = 3.14 * 10^2
area = 3.14 * 100
area ≈ 314
Therefore, the area of the rug is approximately 314 square inches.
The correct answer is C. 314 in2.