Math 7 Accelerated Circles Quiz

1. If the diameter of a circle is 12m, what is the radius of that circle?

The radius of a circle is half of its diameter. Therefore, if the diameter of a circle is 12m, the radius would be half of that, which is 6m.

Explanation

The radius of a circle is half of its diameter. Therefore, if the diameter of a circle is 12m, the radius would be half of that, which is 6m.

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3. If the diameter of a circle is 10m, what is the radius of that circle?

The radius of a circle is half of its diameter. Therefore, if the diameter of the circle is 10m, the radius would be half of that, which is 5m.

Explanation

The radius of a circle is half of its diameter. Therefore, if the diameter of the circle is 10m, the radius would be half of that, which is 5m.

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4. What does it mean to "square" a number?

To multiply a number by itself.

To add a number to itself.

To divide a number by itself.

To subtract a number from itself.

"Squaring" a number means multiplying the number by itself. This is done by taking the number and multiplying it by itself, resulting in the number being squared. For example, squaring 3 would be 3 multiplied by 3, which equals 9.

Explanation

"Squaring" a number means multiplying the number by itself. This is done by taking the number and multiplying it by itself, resulting in the number being squared. For example, squaring 3 would be 3 multiplied by 3, which equals 9.

5. What is the area of a circle with a circumference of $12\pi$ ?

$36\pi$

6

$6\pi$

36

$16\pi$

If the circumference is 12pi, then the diameter is 12, which means the radius is 6. Square the radius to calculate the area. 6 squared is 36. The answer is 36pi.

Explanation

If the circumference is 12pi, then the diameter is 12, which means the radius is 6. Square the radius to calculate the area. 6 squared is 36. The answer is 36pi.

6. What is $\pi$ ?Select all that apply.

An number that begins with 3.14.

The radius of a circle squared.

The diameter multiplied by the circumference of a circle.

The circumference divided by the diameter of a circle.

The correct answers are "A number that begins with 3.14" and "The circumference divided by the diameter of a circle." A number that begins with 3.14 refers to the mathematical constant pi (π), which is approximately equal to 3.14. The circumference divided by the diameter of a circle is also equal to pi (π), as this ratio is constant for all circles.

Explanation

The correct answers are "A number that begins with 3.14" and "The circumference divided by the diameter of a circle." A number that begins with 3.14 refers to the mathematical constant pi (π), which is approximately equal to 3.14. The circumference divided by the diameter of a circle is also equal to pi (π), as this ratio is constant for all circles.

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7. What is the area of the extra-large pizza?

16

16pi

8

8pi

4

4pi

32

32pi

64

64pi

Half of 16 is 8 (the radius). Square the radius (64), then multiply by pi. The answer is 64pi.

Explanation

Half of 16 is 8 (the radius). Square the radius (64), then multiply by pi. The answer is 64pi.

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10. The _____________ of a shape is the number of square units that fit inside a shape

Diameter

Area

Chord

Radius

Circumference

Perimeter

Chord

Please refer to the Educanon video Titled "Circle area".

Explanation

Please refer to the Educanon video Titled "Circle area".

11. The circumference of a circle with radius 8 is ___ times as big as the circumference with radius 1.

The circumference of a circle with a radius 8 is 16pi. The circumference of a circle with radius 1 is 2pi. 16pi divided by 2pi is 8.

Explanation

The circumference of a circle with a radius 8 is 16pi. The circumference of a circle with radius 1 is 2pi. 16pi divided by 2pi is 8.

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12. What is the area of the two medium pizzas combined?

4pi

4

16pi

16

32pi

32

64pi

64

Half the diameter of the 8 inch pizza is 4 (the radius). Square the radius to get 16. The area of one medium pizza is 16pi. The area of two medium pizzas is 2 x 16pi = 32pi.

Explanation

Half the diameter of the 8 inch pizza is 4 (the radius). Square the radius to get 16. The area of one medium pizza is 16pi. The area of two medium pizzas is 2 x 16pi = 32pi.

13. Rope A circles earth while rope B also circles earth but floats 4 meters above the surface of the earth. What is the difference between the lengths of the two ropes?

4pi

4

8

8pi

16pi

16

2pi

2

If the circle floats 4 meters above the surface, then the diameter of this circle is (d+8). Now find the difference of the two circumferences.
(d+8)pi - d pi
d pi + 8pi - dpi
8pi is the answer

Explanation

If the circle floats 4 meters above the surface, then the diameter of this circle is (d+8). Now find the difference of the two circumferences.
(d+8)pi - d pi
d pi + 8pi - dpi
8pi is the answer

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15. Triangle ABC has one side length of 3 and one side length 5, the non-included angle next to the side of length 3 measures 60 degrees. save image

Is there another triangle satisfying these conditions that has a third side of different length?

Yes

No

According to the given information, we have a triangle ABC with side lengths of 3, 5, and an angle of 60 degrees. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. However, in this case, the sum of the lengths of the sides 3 and 5 is equal to 8, which is not greater than any possible length for the third side. Therefore, there is no other triangle that satisfies these conditions with a third side of different length.

Explanation

According to the given information, we have a triangle ABC with side lengths of 3, 5, and an angle of 60 degrees. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. However, in this case, the sum of the lengths of the sides 3 and 5 is equal to 8, which is not greater than any possible length for the third side. Therefore, there is no other triangle that satisfies these conditions with a third side of different length.

16. What is the area of a circle with a circumference of $16\pi$ ?

8

$8\pi$

$32\pi$

32

$64\pi$

64

If the circumference is 16pi, then the diameter is 16, which means the radius is 8. Using the formula A=pi times the radius squared, the radius squared is 64, therefore the area is 64pi.

Explanation

If the circumference is 16pi, then the diameter is 16, which means the radius is 8. Using the formula A=pi times the radius squared, the radius squared is 64, therefore the area is 64pi.

17. Which choice will give you more pizza for your money?

Option 1 - One extra-large pizza

Option 2 - Two medium pizzas

Option 1 offered 64pi worth of pizza. Option 2 offered 32pi worth of pizza.

Explanation

Option 1 offered 64pi worth of pizza. Option 2 offered 32pi worth of pizza.