Answer :
Answer:
460 cm.
Step-by-step explanation:
Explanation(s):
According to this word problem, the circumference of the circle is 76 centimeters.
Now, we know that the formulas for finding circumference is:
[tex]c=\pi d(diameter)/2\pi r(radius)[/tex]
Solve:
I will use the first formula.
To find the diameter of a circle when given only the circumference, divide the circumference by pi (3.14). The quotient is the diameter of the circle.
[tex]76/3.14=24.2038216561[/tex]
24.2038216561 is the diameter.
However, to find the area of the circle, we must have the radius.
The formula for finding the area of a circle is:
[tex]a=\pi r^2[/tex]
Remember, to find the radius of a circle, divide the diameter by 2.
[tex]24.2038216561/2=12.1019108281.[/tex]
Now, that we have the radius, we can find the area of the circle.
[tex]3.14*12.1019108281*12.1019108281=459.872611471.[/tex]
Lastly, round the product, 459.872611471, to the nearest whole number.
[tex]459.872611471[/tex] ≈ [tex]460[/tex]
Conclude:
I, therefore, believe the area of the circle is 460 cm.