Mathematics, 12.08.2020 09:01 ste78

GIVING OUT BRAINLIEST TO THE FIRST PERSON TO ANSWER!! One circle has a diameter of 6 inches. A second, larger circle has a diameter that is four times the diameter of the first circle. What is the ratio of the area of the smaller circle to the larger circle?

A. 2:3

B. 1:6:4

C. 1:16

D. 1:64

Please include ALL work! <3

Answers: 2

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Answer from: alexmoy45p8yd7v

The answer is option C

Step-by-step explanation:

To find the ratio first find the diameter of the larger circle

Diameter of first circle = 6 inches

Diameter of second circle = 4 × diameter of the first circle

Which is

Diameter of second circle

= 4 × 6 = 24 inches

Area of a circle = πr²

r is the radius

Area of smaller circle

Diameter = 6 inches

Radius = 6 / 2 = 3 inches

Area = (3)² π = 9π in²

Area of larger circle

Diameter = 24 inches

Radius = 24 / 2 = 12 inches

Area = (12)²π = 144π in²

The ratio of the smaller circle to the larger circle is

$\frac{9\pi}{144\pi}$

Reduce the fraction by 9π

That's

$\frac{1}{16}$

We have the final answer as

1 : 16

Hope this helps you

Answer from: carmencolon119

C. 1:16

Step-by-step explanation:

Area of a circle is:

$\pi \times {r}^{2}$

Small circle Area:

radius = diameter/2

radius = 6/2 = 3

$area \: of \: a \: circle \: = \pi {3}^{2}$

a = 28.27

Large circle 4 times larger diameter

6*4 = 24

diameter = 24

r = 24/2

r = 12

$a \: = \pi {12}^{2}$

a = 452.39

area of large circle/ area of small circle

452.39/28.27 = 16.00

ratio is 1:16

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GIVING OUT BRAINLIEST TO THE FIRST PERSON TO ANSWER!! One circle has a diameter of 6 inches. A seco...