The number of square units in the area of circle P is equal to the number of units in the circumference of circle P. Assuming that the diameter of the circle must be greater than P, what is the radius of circle P ?
a. 2
b. 2 pi
c. 4
d. 4 pi
e. cannot be determined from the information given
please answer and explain
pi r^2 = 2pi r
divide by pi*r to get
r=2
Since P is a circle, it makes no sense to say the "diameter must be greater than P".
To solve this problem, we need to use the formulas for the area and circumference of a circle.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius of the circle.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle.
According to the problem, the number of square units in the area of circle P is equal to the number of units in the circumference of circle P. In other words, A = C.
Substituting the formulas for A and C into the equation, we get:
πr^2 = 2πr
To find the radius of circle P, we need to solve this equation for r.
By canceling out πr from both sides we get:
r = 2
Therefore, the radius of circle P is 2.
The answer is option a. 2.
Explanation:
To solve this problem, we used the formulas for the area and circumference of a circle and set them equal to each other. We then simplified the equation and solved for the radius.