Question

5)

Calculate the ratio to the nearest hundredth.
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RATIO
U
DIAMETER (d) CIRCUMFERENCE (C)
20 in.
62.83 in.
är
liliom
DE
10 in.
31.41 in.
6
in.
18.84 in.
2
in.
6.28 in.
1
in.
3.14 in.
0
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Complete
A
16% Complete
earch
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Answer 1

To find the ratio of the diameter to the circumference, divide the diameter by the circumference for each given pair of measurements. After calculating, all ratios rounded to the nearest hundredth are approximately 0.32, consistent with the inverse of the mathematical constant π (pi).

Step-by-step explanation:

To calculate the ratio of the diameter (d) to the circumference (C), we divide the diameter by the circumference.

This ratio should be the same for all circles and is the inverse of π (pi), which is approximately 3.14159. We will use the given measurements to find this ratio to the nearest hundredth.

For a 20-inch diameter and 62.83-inch circumference, the ratio is ∑/d = 20/62.83 ≈ 0.32.

For a 10-inch diameter and 31.41-inch circumference, the ratio is d/C = 10/31.41 ≈ 0.32.

For a 6-inch diameter and 18.84-inch circumference, the ratio is d/C = 6/18.84 ≈ 0.32.

For a 2-inch diameter and 6.28-inch circumference, the ratio is d/C = 2/6.28 ≈ 0.32.

For a 1-inch diameter and 3.14-inch circumference, the ratio is d/C = 1/3.14 ≈ 0.32.

The calculated ratios are consistent with the mathematical constant π (pi), which is expected when dividing a circle's diameter by its circumference. In this case, all the ratios, when rounded to the nearest hundredth, are approximately 0.32.

Answer 2

Answer for (a) to (e) = 0.32

Calculate the ratio to the nearest hundredth.

Find the Ratio of Diameter (d) and circumference (C)

Step by step explanation:

In order to determine the ratio we must know the formula for the circumference of a circle. Then relate it to the diameter.

But since we have been the value if both circumference and diameter, we would just calculate the ratio.

Circumference of a circle = 2πr

Where d = diameter = 2r

Circumference = πd

a) d = 20 in.

C = 62.83 in.

Ratio of Diameter (d) and circumference (C) = d:C

= 20/(62.83)

d:C = 0.32

b) d=10 in.

C =31.41 in.

d:C = 10/(31.41)

d:C = 0.32

c) d =6 in.

C =18.84 in.

d:C = 6/(18.84)

d:C = 0.32

d) d= 2 in.

C = 6.28 in.

d:C = 2/6.28

d:C = 0.32

e) d = 1 in.

C = 3.14 in.

d:C = 1/3.14

d:C = 0.32

The above answers indicate that the ratio of a circumference of a circle to its diameter = d/C = d/(π×d)

= 1/π = 0.32