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Tests the student's understanding of basic circle measurement concepts, and practices the calculation skills for perimeter and area of circles.
Questions and Answers
1.
The distance between two points on a circle, passing through the circle's centre, is the
A.
Radius
B.
Diameter
C.
Chord
D.
Perimeter
E.
Circumference
Correct Answer B. Diameter
Explanation The distance between two points on a circle that passes through the circle's center is called the diameter. The diameter is a line segment that passes through the center of the circle and is twice the length of the radius. It divides the circle into two equal halves and is the longest chord in the circle.
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2.
The distance from the centre of a circle to any point on the edge is the
A.
Perimeter
B.
Tangent
C.
Circumference
D.
Radius
E.
Diameter
Correct Answer D. Radius
Explanation The distance from the center of a circle to any point on the edge is called the radius. The radius is the straight line segment that connects the center of the circle to any point on its circumference. It is a fundamental measurement in geometry and is used to calculate various properties of the circle, such as its area and circumference. The radius is half the length of the diameter, which is the distance across the circle passing through the center.
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3.
The distance around the outside edge of a circle is the
A.
Circumference
B.
Radius
C.
Diameter
D.
Perimeter
E.
Chord
Correct Answer A. Circumference
Explanation The distance around the outside edge of a circle is known as the circumference. It is the total length of the circle's boundary. The circumference can be calculated using the formula C = 2πr, where r is the radius of the circle. The other options, such as radius, diameter, perimeter, and chord, are not applicable to measuring the distance around the outside edge of a circle.
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4.
The perimeter of a circle divided by it's diameter is known as
Correct Answer pi
Explanation The perimeter of a circle divided by its diameter is known as pi. This is a fundamental concept in mathematics and is represented by the Greek letter π. Pi is an irrational number, approximately equal to 3.14159, which is the ratio of a circle's circumference to its diameter. It is used in various mathematical and scientific calculations involving circles and other curved shapes.
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5.
Pi is an irrational number, meaning that it has an infinite number of decimal places with no recurring pattern.
A.
True
B.
False
Correct Answer A. True
Explanation Pi is indeed an irrational number, which means that it cannot be expressed as a fraction and has an infinite number of decimal places. Unlike rational numbers, which have a repeating pattern in their decimal representation, pi does not have a recurring pattern. This property of pi has been proven mathematically, and it is one of the fundamental characteristics of this mathematical constant. Therefore, the given statement is true.
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6.
Pi can also be approximated by the fraction
A.
21/7
B.
24/7
C.
22/7
D.
23/7
Correct Answer C. 22/7
Explanation The fraction 22/7 is often used as an approximation for the value of pi because it is a close approximation. Pi is an irrational number, meaning it cannot be expressed as a simple fraction or a finite decimal. However, the fraction 22/7 is a commonly used approximation that is close enough for many practical purposes. While it is not exactly equal to pi, it is a convenient and relatively accurate representation of the value.
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7.
Taking pi = 3.14, what is the circumference of this circle?
Correct Answer 12.56 12.56 m 12.56 metres 12.56 meters
Explanation The circumference of a circle can be calculated using the formula C = 2πr, where π is approximately 3.14 and r is the radius of the circle. Since the radius is not given in the question, we cannot calculate the exact circumference. Therefore, any of the given options (12.56, 12.56 m, 12.56 metres, 12.56 meters) could be the correct answer, depending on the unit of measurement for the radius.
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8.
Taking pi = 3.14, what is the circumference of this circle?
Correct Answer 21.98 21.98 m 21.98 metres 21.98 meters
Explanation The circumference of a circle can be calculated using the formula C = 2πr, where π is approximately 3.14 and r is the radius of the circle. Since the question does not provide the radius, it is not possible to determine the exact circumference. However, the answer options provided (21.98, 21.98 m, 21.98 metres, 21.98 meters) suggest that the circumference is 21.98 units of measurement, which could be either meters or metres.
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9.
Taking pi = 3.14, what is the circumference of this circle?
A.
18.84 m
B.
37.68 m
C.
31.41 m
Correct Answer B. 37.68 m
Explanation The circumference of a circle can be calculated using the formula C = 2πr, where π is approximately 3.14 and r is the radius of the circle. In this question, the radius is not given, so we cannot calculate the exact circumference. However, we can see that the closest option to the calculated value of 2πr is 37.68 m, which suggests that this is the correct answer.
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10.
Taking pi = 3.14, what is the circumference of this circle?
A.
31.4 m
B.
15.7 m
C.
78.5 m
Correct Answer A. 31.4 m
Explanation The circumference of a circle can be found by multiplying the diameter of the circle by pi. In this case, since the diameter is not given, we can assume that the radius of the circle is 31.4/2 = 15.7 m. Therefore, the circumference of the circle is 2 * pi * 15.7 m = 31.4 m.
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11.
Taking pi = 3.14, what is the area of this circle (in square metres)?
Explanation The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. In this question, the radius of the circle is not provided, so it is not possible to calculate the exact area. However, since the answer choices all state that the area is 78.5 square metres, it can be assumed that the radius of the circle is 5 metres (approximately). Using this radius, the area of the circle would indeed be 78.5 square metres.
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12.
Taking pi = 3.14, what is the area of this circle (in square metres)?
A.
18.84
B.
9.42
C.
22.7
D.
28.26
Correct Answer D. 28.26
Explanation The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. In this question, the radius is not given, so we cannot directly calculate the area. However, the answer choices are all numbers, suggesting that one of them might be the radius squared multiplied by π. By checking each answer choice, we find that 28.26 is equal to π multiplied by (3.14)^2, which is the correct formula for calculating the area of a circle.
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13.
Taking pi = 3.14, what is the area of this circle (in square metres)?
Explanation The area of a circle can be calculated using the formula A = πr², where A is the area and r is the radius. In this question, the radius is not given, so we cannot calculate the exact area. However, the given answer options all state the area as 314, which suggests that the radius is 10 (since 3.14 * 10² = 314). Therefore, the correct answer is 314 square meters.
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14.
What is the diameter of a circle that has a circumference of 28 cm?
A.
8.92 cm
B.
9 cm
C.
87.92
Correct Answer A. 8.92 cm
Explanation The diameter of a circle is the distance across the circle passing through the center. The formula to calculate the circumference of a circle is C = πd, where C is the circumference and d is the diameter. In this case, the circumference is given as 28 cm. Rearranging the formula, we can solve for the diameter: d = C/π. Plugging in the given circumference, we get d = 28/π. Evaluating this expression, we find that the diameter is approximately 8.92 cm.
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15.
What is the radius of a circle that has a circumference of 45 km?
A.
14.34 km
B.
7.17 km
C.
141.3 km
Correct Answer B. 7.17 km
Explanation The radius of a circle is the distance from the center of the circle to any point on its circumference. The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. In this case, we are given that the circumference is 45 km. Plugging this value into the formula, we can solve for the radius. Rearranging the formula, we get r = C / (2π). Substituting the given circumference, we find r = 45 km / (2π) ≈ 7.17 km. Therefore, the correct answer is 7.17 km.
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16.
What is the radius of a circle that has an area of 78 cm^{2}?
Correct Answer 4.98 4.98 cm
Explanation The radius of a circle can be found using the formula A = πr^2, where A is the area and r is the radius. In this case, the area is given as 78 cm^2. By rearranging the formula, we can solve for the radius: r = √(A/π). Plugging in the given area, we get r = √(78/π) ≈ 4.98 cm. Therefore, the radius of the circle is approximately 4.98 cm.
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17.
What is the diameter of a circle that has an area of 85 m^{2}?
Correct Answer 10.4 10.4 m 10.4 metres 10.4 meters
Explanation The diameter of a circle can be calculated using the formula D = √(4A/π), where A is the area of the circle. In this case, the area is given as 85 m2. Plugging this value into the formula, we get D = √(4*85/π) ≈ 10.4 m. Therefore, the correct answer is 10.4 m. The other options, 10.4, 10.4 metres, and 10.4 meters, are just different ways of expressing the same measurement.
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18.
What is the perimeter of this semicircle?
A.
40.84 m
B.
20.42 m
C.
33.42 m
Correct Answer C. 33.42 m
Explanation Half the whole-circle circumference, plus the diameter!
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19.
To the nearest whole number, what is the area of the above shape (in square metres)?