Question

Circle a has circumference 223 m. circle b has a diameter that is 112 times as long as circle a’s diameter. What is the circumference of circle b if circle a has a circumference of 223 m, and circle b has a diameter that is 112 times as long as circle a's diameter?

a) 7.94 m
b) 894 m
c) 25056 m
d) 0.02 m

Answer 1

Given the circumference of Circle A is 223 meters, and Circle B's diameter is 112 times Circle A's diameter, we calculate Circle A's diameter, multiply it by 112 to find Circle B's diameter, and then calculate Circle B's circumference by multiplying the diameter by π, resulting in a circumference of 24976 meters.

Step-by-step explanation:

The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter of the circle. If Circle A has a circumference of 223 meters, we can use the formula to find its diameter first. Since Circle B's diameter is 112 times as long as Circle A's diameter, we multiply Circle A's diameter by 112 to obtain Circle B's diameter. Then, we use the circumference formula again to calculate the circumference of Circle B. We can ignore units such as m² or cubic meters here as we are only dealing with linear measurements such as meters.

First, find the diameter of Circle A using the known circumference: A = πd ⇔ d = A / π. Next, determine Circle B's diameter: multiply Circle A's diameter by 112. Finally, find the circumference of Circle B: C = π × (Diameter of Circle B).

Applying these steps:

1. Diameter of Circle A = 223 m / π
2. Diameter of Circle B = (223 m / π) × 112
3. Circumference of Circle B = π × [(223 m / π) × 112]
4. Result: Circumference of Circle B = 223 m × 112

Thus, the circumference of Circle B is 223 m × 112 = 24976 m, which is not one of the provided options, indicating there may be a typo in the question or the provided options.