Mathematics Form 2 - Circle

1) The formulae 2πr, the 'r' stands for

The formula 2πr is used to calculate the circumference of a circle, where r represents the radius of the circle. The radius is the distance from the center of the circle to any point on its edge. Therefore, in the given formula, the 'r' stands for radius.

Explanation

The formula 2πr is used to calculate the circumference of a circle, where r represents the radius of the circle. The radius is the distance from the center of the circle to any point on its edge. Therefore, in the given formula, the 'r' stands for radius.

Submit

2) Look at the picture. What is A?

Chord

Radius

Sector

Diameter

The correct answer is "Radius" because in the picture, A is the line segment that connects the center of the circle to any point on the circumference. The radius is always half the length of the diameter and it helps determine the size and proportions of the circle.

Explanation

The correct answer is "Radius" because in the picture, A is the line segment that connects the center of the circle to any point on the circumference. The radius is always half the length of the diameter and it helps determine the size and proportions of the circle.

3) Is C the diameter of the circle?

Yes

No

The answer is "Yes" because the diameter of a circle is a line segment that passes through the center of the circle and connects two points on the circumference. In this case, if C is the diameter of the circle, it means that it meets the criteria of being a line segment passing through the center, so the answer is "Yes".

Explanation

The answer is "Yes" because the diameter of a circle is a line segment that passes through the center of the circle and connects two points on the circumference. In this case, if C is the diameter of the circle, it means that it meets the criteria of being a line segment passing through the center, so the answer is "Yes".

4) Calculate the circumference of a circle with a diameter 2m. Use π=3.142

6.284m

5.1m

23.1m

4.163m

The circumference of a circle can be calculated by multiplying the diameter by π (pi). In this case, the diameter is given as 2m. So, the circumference would be 2 * 3.142 = 6.284m.

Explanation

The circumference of a circle can be calculated by multiplying the diameter by π (pi). In this case, the diameter is given as 2m. So, the circumference would be 2 * 3.142 = 6.284m.

5) Find diameter of a circle with a circumference of 36cm. Use π=3.142.

13.2cm

17cm

11.5cm

20.2cm

The formula to find the diameter of a circle is circumference divided by π. In this case, the circumference is given as 36cm and π is given as 3.142. By dividing 36 by 3.142, we get approximately 11.5cm, which is the diameter of the circle.

Explanation

The formula to find the diameter of a circle is circumference divided by π. In this case, the circumference is given as 36cm and π is given as 3.142. By dividing 36 by 3.142, we get approximately 11.5cm, which is the diameter of the circle.

6) Calculate the circumference of a circle with a radius of 12cm. Use π = 3.142

34

69.1

75.4

56.51

The formula to calculate the circumference of a circle is 2πr, where r is the radius of the circle. In this case, the radius is given as 12cm. Using the value of π as 3.142, we can substitute the values into the formula and calculate the circumference. 2 * 3.142 * 12 = 75.4. Therefore, the correct answer is 75.4.

Explanation

The formula to calculate the circumference of a circle is 2πr, where r is the radius of the circle. In this case, the radius is given as 12cm. Using the value of π as 3.142, we can substitute the values into the formula and calculate the circumference. 2 * 3.142 * 12 = 75.4. Therefore, the correct answer is 75.4.

7) Calculate the arc length of the sector given in the picture. Use π = 3.142

3.15cm

5.498cm

6.0cm

2.29cm

75 / 360 x (2 π r) = 5.498

Explanation

75 / 360 x (2 π r) = 5.498

8) A round-shaped cake has a circumference of 54 cm. What is the radius of the cake?

4.66cm

6.78cm

8.59cm

8.00cm

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. In this case, we are given that the circumference is 54 cm. Plugging this into the formula, we get 2πr = 54. Solving for r, we find that the radius is approximately 8.59 cm.

Explanation

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. In this case, we are given that the circumference is 54 cm. Plugging this into the formula, we get 2πr = 54. Solving for r, we find that the radius is approximately 8.59 cm.

9) A ball fits exactly into a square box, as shown in the diagram. If the length of the box is 21cm, find the circumference of the circle. Use π = 3.142

70 cm

65.98 cm

56.45 cm

86.43 cm

The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle. In this case, the ball fits exactly into the square box, so the diameter of the circle is equal to the length of the box. The radius of the circle is then half of the diameter, which is 21cm/2 = 10.5cm. Plugging this value into the formula, we get C = 2 * 3.142 * 10.5 = 65.98 cm. Therefore, the circumference of the circle is 65.98 cm.

Explanation

The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle. In this case, the ball fits exactly into the square box, so the diameter of the circle is equal to the length of the box. The radius of the circle is then half of the diameter, which is 21cm/2 = 10.5cm. Plugging this value into the formula, we get C = 2 * 3.142 * 10.5 = 65.98 cm. Therefore, the circumference of the circle is 65.98 cm.

10) Find the radius of a circle with a circumference of 63.5mm. Use π=3.142.

10.11mm

21.5mm

23.5mm

17.5mm

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle. In this case, we are given the circumference as 63.5mm. Rearranging the formula, we can solve for the radius by dividing the circumference by 2π. Using the value of π as 3.142, we can calculate the radius as 63.5mm / (2 * 3.142) = 10.11mm. Therefore, the correct answer is 10.11mm.

Explanation

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle. In this case, we are given the circumference as 63.5mm. Rearranging the formula, we can solve for the radius by dividing the circumference by 2π. Using the value of π as 3.142, we can calculate the radius as 63.5mm / (2 * 3.142) = 10.11mm. Therefore, the correct answer is 10.11mm.