Q. If a circle has a radius of 4 cm, what is the diameter of the circle?
A.
8 cm
B.
12 cm
C.
16 cm
D.
10 cm
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Solution
The diameter of a circle is twice the radius. For a radius of 4 cm, the diameter is 2 * 4 = 8 cm.
Correct Answer:
A
— 8 cm
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Q. If a circle has a radius of 4 units, what is its area?
A.
16π
B.
8π
C.
12π
D.
20π
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Solution
The area of a circle is given by the formula A = πr². Thus, A = π(4)² = 16π.
Correct Answer:
A
— 16π
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Q. If a circle has a radius of 4 units, what is its circumference?
A.
8π units
B.
16π units
C.
12π units
D.
20π units
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Solution
The circumference of a circle is given by the formula C = 2πr. Therefore, C = 2π * 4 = 8π units.
Correct Answer:
A
— 8π units
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Q. If a circle has a radius of 5 cm, what is its area?
A.
25π cm²
B.
50π cm²
C.
75π cm²
D.
100π cm²
Show solution
Solution
The area of a circle is given by the formula A = πr². Thus, A = π(5)² = 25π cm².
Correct Answer:
A
— 25π cm²
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Q. If a circle has a radius of 5 cm, what is its circumference?
A.
10π cm
B.
15π cm
C.
20π cm
D.
25π cm
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Solution
Circumference = 2πr = 2π(5) = 10π cm.
Correct Answer:
A
— 10π cm
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Q. If a circle has a radius of 5 cm, what is the area of the circle?
A.
25π cm²
B.
10π cm²
C.
20π cm²
D.
15π cm²
Show solution
Solution
The area of a circle is given by the formula A = πr². Thus, A = π(5)² = 25π cm².
Correct Answer:
A
— 25π cm²
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Q. If a circle has a radius of 5 cm, what is the area of the sector formed by a 60-degree angle?
A.
13.09 cm²
B.
25.00 cm²
C.
15.71 cm²
D.
20.94 cm²
Show solution
Solution
Area of sector = (θ/360) * πr² = (60/360) * π(5)² = (1/6) * 25π ≈ 13.09 cm².
Correct Answer:
A
— 13.09 cm²
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Q. If a circle has a radius of 5 cm, what is the circumference of the circle?
A.
10π cm
B.
15π cm
C.
20π cm
D.
25π cm
Show solution
Solution
The circumference of a circle is given by the formula C = 2πr. Thus, C = 2π(5) = 10π cm.
Correct Answer:
A
— 10π cm
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Q. If a circle has a radius of 5 cm, what is the circumference of the circle? (Use π ≈ 3.14)
A.
15.7 cm
B.
31.4 cm
C.
78.5 cm
D.
25 cm
Show solution
Solution
The circumference of a circle is given by the formula C = 2πr. Thus, C = 2 * 3.14 * 5 = 31.4 cm.
Correct Answer:
B
— 31.4 cm
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Q. If a circle has a radius of 5 cm, what is the length of a chord that is 4 cm away from the center of the circle?
A.
3 cm
B.
4 cm
C.
6 cm
D.
8 cm
Show solution
Solution
Using the Pythagorean theorem, the length of the chord can be calculated as 2 * sqrt(5^2 - 4^2) = 6 cm.
Correct Answer:
C
— 6 cm
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Q. If a circle has a radius of 5 cm, what is the length of a chord that is 4 cm away from the center?
A.
3 cm
B.
4 cm
C.
6 cm
D.
8 cm
Show solution
Solution
Using the Pythagorean theorem, the length of the chord is 2√(5^2 - 4^2) = 2√9 = 6 cm.
Correct Answer:
A
— 3 cm
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Q. If a circle has a radius of 5 cm, what is the length of a chord that is 6 cm away from the center?
A.
4 cm
B.
6 cm
C.
8 cm
D.
10 cm
Show solution
Solution
Using the Pythagorean theorem, the length of the chord can be calculated as 2 * sqrt(5^2 - 6^2) = 2 * sqrt(25 - 36) = 2 * sqrt(-11), which is not possible. The chord cannot exist.
Correct Answer:
A
— 4 cm
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Q. If a circle has a radius of 5, what is its area?
A.
25π
B.
10π
C.
20π
D.
15π
Show solution
Solution
Area of a circle: A = πr² = π(5)² = 25π.
Correct Answer:
A
— 25π
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Q. If a circle has a radius of 7 cm, what is the area of the circle?
A.
154 cm²
B.
49 cm²
C.
44 cm²
D.
28 cm²
Show solution
Solution
The area of a circle is given by the formula A = πr². Thus, A = π(7)² = 49π ≈ 154 cm².
Correct Answer:
A
— 154 cm²
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Q. If a circle has a radius of 7 cm, what is the circumference of the circle? (Use π ≈ 3.14)
A.
21.98 cm
B.
43.96 cm
C.
14 cm
D.
49 cm
Show solution
Solution
Circumference = 2πr = 2 * 3.14 * 7 = 43.96 cm.
Correct Answer:
B
— 43.96 cm
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Q. If a circle has a radius of 7 cm, what is the length of the circumference?
A.
14π cm
B.
21π cm
C.
49 cm
D.
14 cm
Show solution
Solution
The circumference of a circle is given by the formula C = 2πr. Therefore, C = 2π(7) = 14π cm.
Correct Answer:
A
— 14π cm
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Q. If a circle has a radius of 9 cm, what is the area of the circle?
A.
81π cm²
B.
72π cm²
C.
36π cm²
D.
18π cm²
Show solution
Solution
Area = πr² = π(9)² = 81π cm².
Correct Answer:
A
— 81π cm²
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Q. If a circle has an area of 36π cm², what is its radius?
A.
6 cm
B.
4 cm
C.
3 cm
D.
2 cm
Show solution
Solution
Area = πr²; 36π = πr²; r² = 36; r = 6 cm.
Correct Answer:
A
— 6 cm
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Q. If a circle has an area of 36π cm², what is the radius of the circle?
A.
6 cm
B.
12 cm
C.
9 cm
D.
18 cm
Show solution
Solution
Area = πr², so 36π = πr², r² = 36, r = 6 cm.
Correct Answer:
A
— 6 cm
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Q. If a circle has an area of 36π cm², what is the radius?
A.
6 cm
B.
12 cm
C.
18 cm
D.
9 cm
Show solution
Solution
Area = πr², so 36π = πr², r² = 36, r = 6 cm.
Correct Answer:
A
— 6 cm
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Q. If a circle has an area of 50 cm², what is its radius?
A.
5 cm
B.
7.07 cm
C.
10 cm
D.
8 cm
Show solution
Solution
Area = πr², so r = √(Area/π) = √(50/π) ≈ 7.07 cm.
Correct Answer:
B
— 7.07 cm
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Q. If a circle has an area of 50π cm², what is the radius of the circle?
A.
5 cm
B.
10 cm
C.
7 cm
D.
8 cm
Show solution
Solution
Area = πr², so r² = 50, r = √50 ≈ 7.07 cm.
Correct Answer:
B
— 10 cm
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Q. If a circle has an area of 78.5 cm², what is its radius?
A.
5 cm
B.
7 cm
C.
10 cm
D.
6 cm
Show solution
Solution
Area = πr², so r = √(Area/π) = √(78.5/π) ≈ 5 cm.
Correct Answer:
B
— 7 cm
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Q. If a circle is centered at (2, 3) with a radius of 5, what is the equation of the circle?
A.
(x - 2)² + (y - 3)² = 25
B.
(x + 2)² + (y + 3)² = 25
C.
(x - 2)² + (y + 3)² = 25
D.
(x + 2)² + (y - 3)² = 25
Show solution
Solution
The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Correct Answer:
A
— (x - 2)² + (y - 3)² = 25
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Q. If a circle is inscribed in a quadrilateral, what is the relationship between the lengths of the sides?
A.
Opposite sides are equal
B.
Sum of opposite sides is equal
C.
All sides are equal
D.
Adjacent sides are equal
Show solution
Solution
For a quadrilateral to have an inscribed circle, the sum of the lengths of opposite sides must be equal.
Correct Answer:
B
— Sum of opposite sides is equal
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Q. If a data set has a mean of 10 and a standard deviation of 2, what is the z-score of a value 12?
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Solution
Z-score = (X - mean) / standard deviation = (12 - 10) / 2 = 1.
Correct Answer:
A
— 1
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Q. If a fair six-sided die is rolled, what is the probability of rolling a number greater than 4?
A.
1/6
B.
1/3
C.
1/2
D.
1/4
Show solution
Solution
Numbers greater than 4 are 5 and 6. Probability = 2/6 = 1/3.
Correct Answer:
B
— 1/3
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Q. If a line has a slope of -2 and passes through the point (3, 5), what is its y-intercept?
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Solution
Using the point-slope form: y - y1 = m(x - x1) => y - 5 = -2(x - 3). Setting x = 0 gives y = 1.
Correct Answer:
B
— 3
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Q. If a line has a slope of -3 and passes through the point (2, 5), what is its equation in slope-intercept form?
A.
y = -3x + 11
B.
y = -3x + 5
C.
y = 3x + 5
D.
y = -3x + 2
Show solution
Solution
Using y = mx + b: 5 = -3(2) + b => 5 = -6 + b => b = 11. Thus, y = -3x + 11.
Correct Answer:
A
— y = -3x + 11
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Q. If a line has a slope of -3 and passes through the point (2, 5), what is the y-intercept of the line?
Show solution
Solution
Using the point-slope form: y - 5 = -3(x - 2). Solving for y gives y = -3x + 11, so the y-intercept is 11.
Correct Answer:
A
— 11
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