Biology, 05.10.2019 14:00 Ap621765

Which explanation can be used to derive the formula for the circumference of a circle?

find the relationship between the circumference and the diameter by dividing the length of the circumference and length of the diameter. use this quotient to set up an equation to showing the ratio of the circumference over the diameter equals to ππ . then rearrange the equation to solve for the circumference. substitute 2 times the radius for the diameter.

find the length of the radius and the length of the diameter. then, write a ratio comparing the length of the radius to the diameter. multiply the ratio by ππ and set it equal to the circumference.

find the length of the diameter. square this length and write a ratio for the square of the diameter to the radius. set the ratio equal to the circumference.

find the relationship between the area and the radius. then set up an equation showing the ratio of the area to the radius. substitute the area for 3 times the circumference. finally, rearrange the equation to solve for the circumference.

2. regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. the polygon area can be expressed in terms of the area of a triangle.

let s be the side length of the polygon,

r be the hypotenuse of the right triangle,

h be the height of the triangle, and

n be the number of sides of the regular polygon.

polygon area = n(12sh)n(12sh)

n=6

which statement is true?

as s increases, h approaches r so that rhrh approaches r².

as n increases, h approaches r so that rhrh approaches r².

as r increases, h approaches r so that rhrh approaches r².

as h increases, s approaches r so that rhrh approaches r².

3.what is the area of a circle whose radius is 6 ft?

6π6π ft²

9π9π ft²

36π36π ft²

72π72π ft²

4.the circumference of a circle is 7π7π m.

what is the area of the circle?

3.5π3.5π m²

12.25π12.25π m²

14π14π m²

49π49π m²

Answers: 1

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Answers

The formula for the circumference is derived from this:

Find the relationship between the circumference and the diameter by dividing the length of the circumference and length of the diameter. Use this quotient to set up an equation to showing the ratio of the circumference over the diameter equals to ππ . Then rearrange the equation to solve for the circumference. Substitute 2 times the radius for the diameter.

2. This is true
As n increases, h approaches r so that rhrh approaches r².

3. The are of the circle with radius 6 ft is
36π ft²

4. if the circumference is 7π m, then the diameter is 7 and the radius is 3.5 and the area is
12.25π m²

Answer from: shaylawaldo11

The area of the circle with a radius of 6 ft has been $\rm \bold{36\;\pi \;ft^2}$ . Thus option C is correct. The area of the circle with a circumference $\rm \bold{7\pi}$ has been 12.25 $\rm \bold{\pi \;m^2}$ . Thus, option B is correct.

1. The circumference of the circle and the diameter of the circle ratio can be given by the Archimedes concept.

The ratio of the circumference to the diameter of a circle has been a constant.

The value for the ratio has been equivalent to the value of pi.

Thus, $\rm \dfrac{circumference}{diameter}\;=\;\pi$

We know that, diameter = 2 times of radius

Diameter = 2 $\times$ radius

Substituting D with 2r

Circumference = $\pi$ 2r

C = 2 $\pi$ r.

Thus the circumference of the circle can be given by the relationship between the circumference and the diameter by dividing the length of the circumference and length of the diameter. Use this quotient to set up an equation to show the ratio of the circumference over the diameter equals to $\pi$ . Then rearrange the equation to solve for the circumference. Substitute 2 times the radius for the diameter. Thus option A is correct.

2. While deriving the area of the circle with the inscription of a polygon, the area of the polygon has n corresponding to h.

So, with the increase in n there has been increased in the h approaching r so that rhrh approaches $\rm r^2$ . Thus statement B is true.

3. Area of the circle has been given by:

Area = $\pi$ $\rm r^2$

Area = 3.14 $\rm \times\;(6)^2$

Area = 3.14 $\times$ 36 sq. ft

Area = 36 $\pi$ $\rm ft^2$ .

The area of the circle with a radius of 6 ft has been $\rm \bold{36\pi ft^2}$ . Thus option C is correct.

4. Circumference = $\pi$ $\times$ diameter

7 $\pi$ = circumference

Diameter = 7 m.

Radius = 3.5 m

Area = $\rm \bold{\pi r^2}$

Area = $\rm \pi \;(3.5)^2$

Area = 12.25 $\rm \bold{\pi \;m^2}$ .

The area of the circle with a circumference $\rm \bold{7\pi}$ has been 12.25 $\rm \bold{\pi \;m^2}$ . Thus, option B is correct.

For more information about the circumference and area of a circle, refer to the link:

link

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