If a diameter of a circle (which is 18 inches) is tripled, can the expression 9 (254.34 in square) be used to find the new circle?
I know the answer is yes but I can't figure out how you work it! I come with 9(1,107.36 in square) but apparently that is not correct....
Would someone explain how they got this answer?
I have a quiz over it tomorrow.
Thank you
Daniel
To answer this question, we first need to understand the relationship between the diameter of a circle and its area. The formula to calculate the area of a circle is A = πr^2, where A represents the area and r represents the radius.
In this case, we are given the diameter, which is 18 inches. To find the radius, we divide the diameter by 2: 18 / 2 = 9 inches. Now, we can use this radius to calculate the initial area of the circle.
A = πr^2 = π(9^2) = 81π square inches.
Now, we need to triple the diameter, which means the new diameter will be 18 x 3 = 54 inches. Again, we divide this by 2 to find the new radius: 54 / 2 = 27 inches.
To find the area of the new circle, we use the formula:
A = πr^2 = π(27^2) = 729π square inches.
If we want to calculate the exact area of the new circle, we can use 3.14 as an approximation for π. Therefore,
A ≈ 3.14 x 729 = 2,285.86 square inches.
So, the expression 9(254.34 in square) is not the correct answer. The area of the new circle is approximately 2,285.86 square inches.
I hope this explanation helps you! Good luck with your quiz tomorrow!