Answer:
75.4 (nearest tenth)
Step-by-step explanation:
The diameter of a circle is the distance from one side of the circle to the other through the center. The diameter is the widest part of the circle.
The radius of a circle is the distance from the center to the circumference. The radius is half the diameter of a circle.
We have been given the radius of the circle on the left: r = 4x.
Therefore, as the diameter is twice the radius, the diameter of the circle on the left is: d = 2(4x) = 8x
We have been given the diameter of the circle on the right: d = 6x + 6
Equate the two diameters and solve for x:
⇒ 8x = 6x + 6
⇒ 8x - 6x = 6x + 6 - 6x
⇒ 2x = 6
⇒ 2x ÷ 2 = 6 ÷ 2
⇒ x = 3
Substitute the found value of x into one of the diameter expressions to find the diameter of both circles:
⇒ d = 8x
⇒ d = 8(3)
⇒ d = 24
Circumference of a circle
C = πd
(where d is the diameter)
Substitute the found diameter into the circumference formula:
⇒ C = πd
⇒ C = 24π
⇒ C = 75.39822...
⇒ C = 75.4 (nearest tenth)
Therefore, the circumference of each circle is 75.4 units (nearest tenth).
