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1. What is the area of a circle with a diameter of 12.6 in.?

Use 3.14 for pi and round your final answer to the nearest hundredth.

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

a. Find the difference between the length of the circumference and diameter. Set up an equation showing the relationship of the circumference to diameter to the difference. Rearrange the equation to solve for the circumference. Substitute the diameter with 2 times the radius.

b. First find the relationship of the circumference to its diameter by finding that the length of the diameter wraps around the length of the circumference approximately ​ π ​ times. Use this relationship to write an equation showing the ratio of circumference to diameter equaling ​ π ​ . Then rearrange the equation to solve for the circumference. Substitute the diameter for 2 times the radius.

c. Find the length of the diameter and double this length. Multiply this length by ​ π ​ and set equal the to the circumference. Substitute the diameter for 2 times radius.

d. Find the ratio of the diameter to the area of the circle. Use this ratio to set up an equation to show this ratio equaling ​ π ​. Substitute the area with 3 times the circumference. Then rearrange the equation to equal to the circumference.

3. the attatchment below.

4. What is the area of a circle whose radius is 4 ft?

a 4π ft²
b 8π ft²
c 16π ft²
d 64π ft²

5. The circumference of a circle is 7π m.

What is the area of the circle?

a ​ 3.5π ​ m²
b ​ 12.25π ​ m²
c ​ 14π ​ m²
c ​ 49π ​ m²

1 What is the area of a circle with a diameter of 126 in Use 314 for pi and round your final answer to the nearest hundredth 2 Which explanation can be used to class=

Respuesta :

calculista

Answer:

Part 1) [tex]A=124.63\ in^{2}[/tex]

Part 2) Option b

Part 3)  As n increases,  ns get closer to [tex]2\pi r[/tex]  

Part 4) Option c [tex]16\pi\ ft^{2}[/tex]

Part 5) Option b. [tex]12.25\pi\ m^{2}[/tex]

Step-by-step explanation:

Part 1) What is the area of a circle with a diameter of 12.6 in.?

we know that

the area of a circle is equal to

[tex]A=\pi r^{2}[/tex]    

we have

[tex]r=12.6/2=6.3\ in[/tex] -----> the radius is half the diameter

substitute the values

[tex]A=(3.14)(6.3^{2})=124.63\ in^{2}[/tex]  

Part 2) Which explanation can be used to derive the formula for the circumference of a circle?

First find the relationship of the circumference to its diameter by finding that the length of the diameter wraps around the length of the circumference approximately ​ π ​ times.

Use this relationship to write an equation showing the ratio of circumference to diameter equaling ​ π

so

[tex]\frac{C}{D}=\pi[/tex]

Rearrange the equation to solve for the circumference

[tex]C=\pi D[/tex]

Substitute the diameter for 2 times the radius

[tex]D=2r[/tex]

[tex]C=2\pi r[/tex]                      

Part 3)  we know that

If n increases

then

the product ns get closer to the circumference of the circle

so

the circumference of a circle is equal to [tex]C=2\pi r[/tex]  

therefore

As n increases,  ns get closer to [tex]2\pi r[/tex]        

Part 4) What is the area of a circle whose radius is 4 ft?

we know that

the area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=4\ ft[/tex]

substitute the values

[tex]A=(\pi)(4^{2})=16\pi\ ft^{2}[/tex]

Part 5) The circumference of a circle is 7π m.

What is the area of the circle?

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]C=7\pi\ m[/tex]

substitute and solve for r

[tex]7\pi=2\pi r[/tex]

[tex]r=3.5\ m[/tex]

Find the area of the circle

the area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

substitute

the area of a circle is equal to

[tex]A=\pi (3.5^{2})=12.25\pi\ m^{2}[/tex]

akposevictor

Applying the formula of area and circumference of a circle, therefore:

1. [tex]\mathbf{Area = 124.63 $ in.^2}[/tex]

2. Option B.

3. as n increases, [tex]ns[/tex] gets closer to [tex]2 \pi r[/tex] (option C)

4. c. 16π ft²

5. [tex]\mathbf{A = 12.25 \pi}[/tex]

1. Area of a circle is given by the formula: [tex]A = \pi r^2[/tex]

Thus, if dimeter of a circle = 12.6 in.

radius = half of 12.6 in. = 6.3 in.

  • Area = [tex]3.14 \times 6.3^2 = 124.63 $ in.^2[/tex] (to nearest hundredth).

2. The best explanation on how to derive formula of the circumference of a circle is given in option b.

  • Thus, circumference of a circle is given as: [tex]\mathbf{C = 2 \pi r}[/tex]

3. Given that n is the number of sides of a polygon, and s is the side length of the polygon, therefore, the product of n and s will give us a value that is approximately closer the the value of the circumference of a circle, C.

  • Therefore, as n increases, [tex]ns[/tex] gets closer to [tex]2 \pi r[/tex] (option C)

4. radius of circle = 4 ft

  • Area of the circle = [tex]\pi \times 4^2 = 16 \pi[/tex] (option C)

5. Circumference of a circle = 7π m

To find the area, first, find the radius (r) using the circumference formula.

  • Thus,

[tex]C = 2 \pi r[/tex]

  • Substitute

[tex]7 \pi = 2 \pi r\\\\[/tex]

  • Divide both sides by 2π

[tex]\frac{7 \pi}{2 \pi} = \frac{2 \pi r}{2 \pi} \\\\3.5 = r\\\\\mathbf{r = 3.5 }[/tex]

Find the area

[tex]A = \pi r^2[/tex]

  • Substitute

[tex]A = \pi \times 3.5^2\\\\\mathbf{A = 12.25 \pi}[/tex] (option b)

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