the area of a circle is 78.5 square feet. what is the circumference select all that apply.
A. 5 (pi symbol) feet
B. 10 (pi symbol) feet
C. 20 (pi symbol) feet
D. 15.7 feet (my answer)
E. 31.4 feet
F. 62.8 feet
area = 78.5 = πr^2
r^2 = 78.5/π
r = √(78.5/π) = appr. 4.9987
C = 2πr = appr 9.9975π , I see 10π which would be a choice
= appr 31.4079.., I see 31.4, which would be another choice,
so I would say B and E
To find the circumference of a circle, you can use the formula:
Circumference = 2 * π * radius
Since the area of the circle is given as 78.5 square feet, you can find the radius using the formula:
Area = π * radius^2
Given Area = 78.5 square feet, you can rearrange the formula to solve for the radius:
radius^2 = Area / π
radius^2 = 78.5 / π
radius^2 ≈ 25
radius ≈ √25
radius ≈ 5 feet
Now, you can calculate the circumference using the formula:
Circumference = 2 * π * radius
Circumference ≈ 2 * π * 5
Circumference ≈ 10 * π
The options given are:
A. 5π feet
B. 10π feet
C. 20π feet
D. 15.7 feet
E. 31.4 feet
F. 62.8 feet
The correct options are:
B. 10π feet
E. 31.4 feet
F. 62.8 feet
Therefore, the correct answers are B, E, and F.
To find the circumference of a circle, you can use the formula:
Circumference = 2 * π * r,
Where π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
Given that the area of the circle is 78.5 square feet, we can use the formula for the area of a circle:
Area = π * r^2.
By rearranging this formula, we can solve for the radius:
r^2 = Area / π,
r = √(Area / π).
Let's calculate the radius:
r = √(78.5 / 3.14159)
r ≈ √(24.961478)
r ≈ 4.996872791.
Now, we can substitute the value of the radius into the circumference formula:
Circumference = 2 * π * 4.996872791.
Calculating the value:
Circumference ≈ 31.415926535.
Rounded to the nearest tenth, the circumference is approximately 31.4 feet.
Therefore, the correct answer is:
E. 31.4 feet.