II.Directions: Solve the following problems. 1. The diameter of a bicycle wheel is 50 cm. What is the area of the wheel? 2. The diameter of a circular top is 4.8 meters. If you put a tablecloth on top of it, how much material do you need? 3. A circular pond has a radius of 4 m. How much materials will be needed if a fence will be put up? 4. The radius of a circle is 9 in. What is the area? 5. What is the area of a circulat center table with a radius of 5.5 meters?
Answers & Comments
Answer:
1.The area of the wheel can be calculated using the formula for the area of a circle, A = πr^2, where r is the radius of the circle. Since the diameter of the wheel is 50 cm, the radius is half of that, or 25 cm.
A = π(25 cm)^2
A = 625π cm^2
Therefore, the area of the wheel is 625π square centimeters.
2.The area of the circular top can be calculated in the same way as problem 1, using the formula A = πr^2. Since the diameter of the top is 4.8 meters, the radius is half of that, or 2.4 meters.
A = π(2.4 m)^2
A = 18.14π m^2
Therefore, you need 18.14π square meters of material to cover the top with a tablecloth.
3.The perimeter of the circular pond can be calculated using the formula for the circumference of a circle, C = 2πr, where r is the radius of the circle. Since the radius of the pond is 4 m, the circumference is:
C = 2π(4 m)
C = 8π m
To fence around the pond, you need enough material to cover the circumference of the pond, which is 8π meters.
4.The area of the circle can be calculated using the formula A = πr^2, where r is the radius of the circle. Since the radius of the circle is 9 inches:
A = π(9 in)^2
A = 81π in^2
Therefore, the area of the circle is 81π square inches.
5.The area of the circular center table can be calculated using the formula A = πr^2, where r is the radius of the circle. Since the radius of the table is 5.5 meters:
A = π(5.5 m)^2
A = 95.03π m^2
Therefore, the area of the circular center table is 95.03π square meters.