Use 3.14 for π. Round answers to the nearest hundredth if necessary.
The figure shows a circle with a point Upper X labeled at the center.
Calculate the area of Circle X if the diameter is 13 inches.
____ square inches
Calculate the radius of Circle X if the circumference is 138.16 square millimeters.
______millimeters
138.16
To calculate the area of a circle, you need to use the formula: A = π * r^2, where A represents the area, π represents pi, and r represents the radius of the circle.
In the given question, the diameter of Circle X is 13 inches, so we need to find the radius first.
The radius (r) is half of the diameter, so r = 13 / 2 = 6.5 inches.
Now we can substitute the value of radius into the formula.
A = π * r^2
A = 3.14 * (6.5)^2
Calculating this, we get:
A ≈ 3.14 * 42.25
A ≈ 132.665
Rounding the answer to the nearest hundredth, the area of Circle X is approximately 132.67 square inches.
Moving on to the second question, to find the radius of a circle when given the circumference, you need to use the formula: C = 2 * π * r, where C represents the circumference, π represents pi, and r represents the radius of the circle.
In the given question, the circumference is 138.16 square millimeters. We need to find the radius (r).
First, isolate the radius term in the formula:
C = 2 * π * r
r = C / (2 * π)
Substituting the given values into the formula:
r = 138.16 / (2 * 3.14)
Calculating this, we get:
r ≈ 138.16 / 6.28
r ≈ 22.01
Rounding the answer to the nearest hundredth, the radius of Circle X is approximately 22.01 millimeters.
Since 3.14 is the standard number for pi in middle school, you would need that to multiply to the radius. 3.14 times ____(whatever is the radius) or sometimes it could be 2 times 3.14 times _____(whatever is the diameter). Just multiply your diameter to your "pi" then round it to the nearest hundredth if needed.
Basic formulas to remember:
d=2r
r=d/2
c=pi2r
c=2pir
d=c/pi
c=pid
Hope this helped!(or not-)
*If this was difficult or hard to understand from this comment, just search up circle fundamentals and learn the circumference steps!
Aaa
Thanks!
(a) recall that area = πr^2
r = 13/2, so area = π * (13/2)^2
(b) recall that C = 2πr
2πr = 138.16, so r = 138.16 / 2π