Question

The circumference of a circle is 8π cm. What is the DIAMETER of the circle?A)2 cmB)4 cmC)6 cmD)8 cm7) If you know the radius, r, of a circle, what do you multiply r by to get the circle's CIRCUMFERENCE?A)2B)πC)2πD)3π8) Allison has five different sized circular cans. She measures their diameters and calculates their circumferences. Which statement correctly describes what she did for each can?A)Add 3.14 to the diameter to find the circumference.B)Divide the diameter by 3.14 to find the circumference.C)Subtract 3.14 to the diameter to find the circumference.D)Multiply the diameter by 3.14 to find the circumference.9) Devin is asked to write out how to find the circumference of a circle. He writes:
"First measure the radius, then multiply that by 2, then multiply that answer by π, and that will give you the circumference."

Which statement is ANOTHER correct response?A)First measure the radius then multiply that by π to find the circumference.B)First measure the diameter then multiply that by π to find the circumference.C)First measure the radius, then divide that by 2, then multiply that answer by π to find the circumference.D)First measure the diameter, then divide that by 2, then multiply that answer by π to find the circumference.10) The circumference of a circle is 65π. In terms of pi, what is the area of the circle?A)600 πB)936.5 πC)950.25 πD)1056.25 πEliminatewill give 100 pts if someone could help me with 5 questions

Answer 1

Q6. The answer is D)8 cm.

The circumference (C) of a circle with radius r is: C = 2r π
The diameter (d) of a circle is double its radius r: d = 2r

Therefore, the circumference of a circle can be written as: C = d π

If the circumference of a circle is 8π cm: C = 8π cm, then
C = d π = 8π cm
d π = 8π cm

Divide π from both sides:
d π / π = 8π cm / π
d = 8 cm
Thus, the diameter of the circle is 8 cm.


Q7. The answer is C) 2π

The circumference (C) of a circle with radius r is: C = 2 r π
Therefore, if r is known, to calculate C, 2π must be added to r.

For example, r = 4
C = 4 * 2π = 8π


Q8. The answer is D)Multiply the diameter by 3.14 to find the circumference

The circumference of a circle is:
C = 2r π
C - the circumference
r - the radius
π = 3.14 (mathematical constant)

However, the diameter of a circle is twice of its radius:
d = 2r
Hence, the circumference can be expressed as: C = d * π

Since Allison knows the diameter of the circle, she must multiply it by π to get the circumference, i.e. she must multiply the diameter by 3.14 (since π = 3.14)


Q9. The answer is B)First measure the diameter then multiply that by π to find the circumference.

The first Devin's statement "First measure the radius (r), then multiply that by 2, then multiply that answer by π, and that will give you the circumference (C)." can be expressed as:
r * 2 * π = C

But, it should be taken into consideration that the sum of two radius (r) is the diameter (d) of the circle: d = 2r

So, C = 2 r π = d π

So, another statement should be: "First measure the diameter then multiply that by π to find the circumference.";
d * π = C


Q10. The answer is D)1056.25 π

The circumference (C) of the circle with radius r is:
C = 2r π

C = 65 π
2r π = 65 π

Divide both sides by π:
2r π / π = 65 π / π
2r = 65
r = 65/2
r = 32.5

The area (A) of the circle with radius r is:
A = r²π
r = 32.5

A = (32.5)²π
A = 1056.25 π

Answer 2

Answer:

1)

The circumference of a circle is 8π cm. What is the DIAMETER of the circle?

Let d denotes the diameter of circle and r it's radius.

We know that diameter of circle is given as:

d=2r

Also the circumference(C) is given by:

C=8π cm.

$C=2\pi r\\\\C=\pi \times 2r\\\\C=\pi\times d\\\\d=\dfrac{C}{\pi}\\\\\d=\dfrac{8 \pi}{\pi}\\\\d=8$

Hence the diameter of circle is:

d=8 cm.

Hence option D is correct.

2)

If you know the radius, r, of a circle, what do you multiply r by to get the circle's CIRCUMFERENCE?

We know that the circumference(C) of a circle is given by:

$C=2\pi r$

Hence we have to multiply 2π to the radius to obtain the circumference of the circle.

Hence option C is correct.

3)

Allison has five different sized circular cans. She measures their diameters and calculates their circumferences. Which statement correctly describes what she did for each can?

As the diameter(d) is given by d=2r where r represents it's radius.

Hence we have to multiply the diameter by 3.14 to obtain the circumference.

(As circumference of a circle is given by:

C=2πr=π×(2r)=π×d

and π=3.14)

Hence option D is true.

4)

Devin is asked to write out how to find the circumference of a circle. He writes:

"First measure the radius, then multiply that by 2, then multiply that answer by π, and that will give you the circumference."

Which statement is ANOTHER correct response?

B) First measure the diameter then multiply that by π to find the circumference.

Since diameter(d) is represented as:

d=2r ; where r is the radius of the circle. (As circumference of a circle is given by:

C=2πr=π×(2r)=π×d )

Hence option B is correct.

5)

The circumference of a circle is 65π. In terms of pi, what is the area of the circle?

We know that the circumference(C) of circle is given by:

$C=2\pi r$

i.e. $2\pi r=65 \pi\\\\r=\dfrac{65}{2}$

Also the area(A) of circle is given by:

$A=\pi r^2\\\\A=\pi\times (\dfrac{65}{2})^2\\\\A=1056.25 \pi$

Hence, option D is correct.