The area of a round mat is 64 pie square inches. What is the diameter of the mat?
√64 = 8
2 * 8 = 16 diameter
To find the diameter of the round mat, we need to first understand the formula for the area of a circle and then rearrange the formula to solve for the diameter.
The formula for the area of a circle is:
Area = π * r^2
Where:
- Area is the total surface area of the circle
- π (pi) is a mathematical constant approximately equal to 3.14159
- r is the radius of the circle
Since we have the area of the circle given as 64π square inches, we can rewrite the formula as:
64π = π * r^2
Now, we can cancel out π on both sides of the equation:
64 = r^2
To solve for r, we can take the square root of both sides:
√64 = √r^2
8 = r
Now, we know that the radius (r) is 8 inches. To find the diameter, we need to multiply the radius by 2:
Diameter = 2 * r
Diameter = 2 * 8
Diameter = 16 inches
Therefore, the diameter of the mat is 16 inches.