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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.

Respuesta :

Omeun
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.
Cricetus

Answer:

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

Step-by-step explanation:

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

[tex]A_a, A_b, C_a, C_b , r_a , r_b[/tex]

Part 1.

[tex]A_a=25A_b\\\pi*r_a^{2}=25\pi*r_b^{2}\\r_a^{2}=25r_b^{2}\\r_a=5r_b[/tex]

Part 2.

[tex]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\\[/tex]

Part3.

[tex]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\\[/tex]

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