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Answer :
The area of the hub cap is approximately 521.5772 square centimeters. A smaller circumference would result in a proportionally smaller area due to the relationship with radius.
To find the area of the hub cap, we'll use the formula for the circumference of a circle and then use that to find the radius and finally the area.
Given:
Circumference = 80.89 cm
Pi (π) = 3.14
We know that the circumference (C) of a circle is given by the formula:
C = 2πr
Where r is the radius of the circle.
Given our circumference is 80.89 cm:
80.89 = 2 × 3.14 × r
r = 80.89 / (2 × 3.14)
r ≈ 12.88 cm (approximately)
Now, we have the radius (r), we can find the area (A) of the hub cap using the formula:
A = πr^2
Plugging in the value of r:
A ≈ 3.14 × (12.88)^2
A ≈ 3.14 × 165.98
A ≈ 521.5772 cm² (approximately)
So, the area of the hub cap is approximately 521.5772 square centimeters.
Now, if the circumference of the hub cap were smaller, it would mean the radius would be smaller. This would decrease the area of the hub cap since the area of a circle is directly proportional to the square of its radius. So, a smaller circumference would result in a smaller hub cap area.
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