Question

The area of circle A is 25 times greater than the area of circle B. Which of the following statements is true?

a. The radius of circle A is 5 times greater than the radius of circle B.
b. The radius of circle A is 25 times greater than the radius of circle B.
c. The radius of circle B is 5 times greater than the radius of circle A.
d. The radius of circle B is 25 times greater than the radius of circle A.

The circumference of circle A is 3 times greater than the circumference of circle B. What is the relationship between the areas of the circles?
a. The area of circle A is 9 times greater than the area of circle B.
b. The area of circle B is 9 times greater than the area of circle A.
c. The area of circle A is 3 times greater than the area of circle B.
d. The area of circle B is 3 times greater than the area of circle A.


The radius of circle A is 6 times greater than the radius of circle B. Which of the following statements is true?
a. The area of circle B is 6 times greater than the area of circle A.
b. The area of circle A is 36 times greater than the area of circle B.
c. The area of circle B is 36 times greater than the area of circle A.
d. The area of circle A is 6 times greater than the area of circle B.

Answer 1

A.The radius of circle A is 5 times greater than the radius of circle B.

C. The area of circle A is 3 times greater than the area of circle B.

D. The area of circle A is 6 times greater than the area of circle B.

Answer 2

1. c) 2. a) 3. b)

Explanation:

Let the Area , Circumference and radius of two circles A and B be

`A_a, A_b, C_a, C_b , r_a , r_b`

Part 1.

`A_a=25A_b\\\pi*r_a^(2)=25\pi*r_b^(2)\\r_a^(2)=25r_b^(2)\\r_a=5r_b`

Part 2.

`C_a= 3C_b\\2\pi*r_a=3*2\pi*r_b\\r_a=3r_b\\squaring \\r_a^(2)=9r_b^(2)\\\pi*r_a^(2)=9*\pi*r_b^(2)\\A_a=9*A_b\\`

Part3.

`r_a=6r_b\\squaring \\r_a^(2)=36r_b^(2)\\\pi*r_a^(2)=\pi*36r_b^(2)\\\pi*r_a^(2)=36\pi*r_b^(2)\\A_a=36A_b\\`