Answer:
A = 483.42 cm^2
Step by step solved:
To find the area of the hub cap, we can use the formula for the circumference of a circle and rearrange it to solve for the radius:
C = 2πr
r = C / 2π
We can substitute the given circumference of 77.93 centimeters and use 3.14 for π:
r = 77.93 cm / (2 × 3.14) ≈ 12.41 cm
Now that we have the radius, we can use the formula for the area of a circle:
A = πr^2
Substituting the value of r we found, we get:
A = 3.14 × (12.41 cm)^2 ≈ 483.42 cm^2
Therefore, the area of the hub cap is approximately 483.42 square centimeters.
Explanation to the Answer:
If the circumference of the hub cap were smaller, the radius of the hub cap would also be smaller, since they are directly proportional. As a result, the area of the hub cap would also be smaller, since it is proportional to the square of the radius.