The radius of circle A is 9 times greater than the radius of circle B. Which of the following statements is true?
A.The area of circle B is 9 times greater than the area of circle A.
B.The area of circle A is 9 times greater than the area of circle B
C.The area of circle B is 81 times greater than the area of circle A.
D.The area of circle A is 81 times greater than the area of circle B.
no, the answer is d)
let the radius of first circle be r
area = πr62
let the area of 2nd circle be 9r
area =π(9x)^2 = 81πr^2, which is 81 times larger.
To compare the areas of the two circles, we need to consider the formula for the area of a circle, which is A = π𝑟² (where A represents the area and r represents the radius).
Let's assume the radius of circle B is x. According to the statement, the radius of circle A is 9 times greater than the radius of circle B, so the radius of circle A is 9x.
Now we can calculate the areas of the two circles:
Area of circle B = πx²
Area of circle A = π(9x)² = π(81x²) = 81πx²
Comparing the two areas, we see that the area of circle A is 81 times greater than the area of circle B.
Therefore, the correct statement is: D. The area of circle A is 81 times greater than the area of circle B.
To determine which statement is true, we need to compare the areas of circles A and B.
The area of a circle is given by the formula A = πr², where A is the area and r is the radius.
Given that the radius of circle A is 9 times greater than the radius of circle B, we can represent this relationship as r(A) = 9r(B).
To compare the areas, we substitute the value of the radius of circle A into the area formula:
A(A) = π(9r(B))² = 81πr(B)²
This tells us that the area of circle A is 81 times greater than the area of circle B.
Therefore, the correct statement is D. The area of circle A is 81 times greater than the area of circle B.