If the number of square inches in the area of a circle is equal to the number of inches in its circumference,the diameter of the circle is
a. 4 inches
b. 2 inches
c. 1 inches
d. pi inches
e. 2 pi inches
please answer and explain
2. i give u the answer, u figure ohh explanation urself.
To solve this problem, we need to understand the formulas for finding the area and circumference of a circle.
The formula for the area of a circle is given by:
Area = πr^2, where π is approximately equal to 3.14 and r is the radius of the circle.
The formula for the circumference of a circle is given by:
Circumference = 2πr, where π is approximately equal to 3.14 and r is the radius of the circle.
In this problem, we are given that the area of the circle is equal to the circumference of the circle. Mathematically, we can represent this as:
πr^2 = 2πr
We can simplify this equation by dividing both sides by π:
r^2 = 2r
Now, let's solve for r by subtracting 2r from both sides of the equation:
r^2 - 2r = 0
Factoring out an r:
r(r - 2) = 0
Using the zero-product property, we know that either r = 0 or (r - 2) = 0.
If r = 0, it would mean that the circle has no radius and no diameter, which is not possible. Therefore, we can ignore this solution.
If (r - 2) = 0, we can solve for r:
r - 2 = 0
r = 2
Now that we have the radius (r), we need to find the diameter (d) of the circle. The diameter is simply twice the radius, so:
d = 2r
d = 2(2)
d = 4
Therefore, the diameter of the circle is 4 inches.
So, the correct answer is option a. 4 inches.
To summarize:
1. Start with the formulas for area and circumference: Area = πr^2, Circumference = 2πr.
2. Set the area equal to the circumference and simplify the equation.
3. Solve for r by factoring the equation.
4. Get the diameter by multiplying the radius by 2.
5. The diameter of the circle is 4 inches.
so πr^2 = 2πr
divide by π and bring the 2r over
r^2 - 2r = 0
r(r - 2)
r = 0 or r = 2
r = 0 would be no circle
r = 2, then diameter is 4