Question

A large circular plate has a radius of 20 centimeters. A small circular plate with a circumference of (20π) centimeters is placed in the center of the larger plate. What is the area of the larger dinner plate that is not covered by the smaller plate?

a. (400π ,cm²)
b. (300π ,cm²)
c. (200π ,cm²)
d. (100π ,cm²)

Answer 1

The area of the large circular plate not covered by the smaller plate is 300π cm².

Step-by-step explanation:

The problem is to find the area of the large circular plate that is not covered by the smaller plate. First, we calculate the area of the large plate. Using the formula for the area of a circle, A = πr², where r is the radius, the area of the large plate is π(20 cm)² = 400π cm². Next, we determine the radius of the smaller plate. Since the circumference C is given by C = 2πr,

and the circumference of the small plate is 20π cm, we can solve for the radius r: 20π cm = 2πr → r = 10 cm. Therefore, the area of the smaller plate is π(10 cm)² = 100π cm². Finally, the uncovered area is the area of the large plate minus the area of the small plate: 400π cm² - 100π cm² = 300π cm².