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Students will be given a measure to represent the diameter, radius or circumference of a circle. Using the given information, they will find the other two measures. Answers should be given in one of the following 3 formats to be considered correct: separated by "and" (A and B), separated by 1 space (A B), or separated by 2 spaces (A B). Other variations may not be recognized by system.
Questions and Answers
1.
If the radius is 12 cm, find the diameter _____ and the circumference _____ of the same circle.
Explanation The diameter of a circle is always twice the length of its radius, so if the radius is 12 cm, the diameter would be 2 times 12 cm, which equals 24 cm. The circumference of a circle can be found using the formula C = πd, where d is the diameter. Substituting the value of the diameter (24 cm) into the formula, we get C = π * 24 cm, which simplifies to C = 24π cm. Since the value of π is approximately 3.14, the circumference of the circle would be approximately 24 * 3.14 cm, which is approximately 75.36 cm.
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2.
BIf the diameter is 12 cm, find the radius _____ and the circumference _____ of the same circle.
Explanation The diameter of a circle is twice the length of its radius. Therefore, if the diameter is 12 cm, the radius would be half of that, which is 6 cm. The circumference of a circle can be found using the formula C = 2πr, where r is the radius. Plugging in the value of the radius (6 cm) into the formula, we get C = 2π(6) = 12π ≈ 37.68 cm.
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3.
If the radius is 5 cm, find the diameter _____ and the circumference _____ of the same circle.
Explanation The diameter of a circle is equal to twice the radius, so if the radius is 5 cm, the diameter would be 2 * 5 cm = 10 cm. The circumference of a circle is given by the formula C = 2 * π * r, where π is a constant approximately equal to 3.14. Plugging in the radius of 5 cm, the circumference would be 2 * 3.14 * 5 cm = 31.4 cm. Therefore, the correct answer is 10 and 31.4.
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4.
If the diameter is 11 cm, find the radius _____ and the circumference _____ of the same circle.
Explanation The diameter of a circle is twice the length of its radius. Therefore, if the diameter is 11 cm, the radius would be half of that, which is 5.5 cm. The circumference of a circle can be found using the formula C = 2πr, where r is the radius. Plugging in the value of the radius, the circumference would be 2π(5.5) = 11π ≈ 34.54 cm.
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5.
If the radius is 6.75 cm, find the diameter _____ and the circumference _____ of the same circle.
Explanation The diameter of a circle is twice the length of its radius, so if the radius is 6.75 cm, the diameter would be 2 * 6.75 cm = 13.5 cm. The circumference of a circle can be found using the formula C = 2 * π * r, where r is the radius. Plugging in the value of the radius (6.75 cm) into the formula, we get C = 2 * 3.14 * 6.75 cm = 42.39 cm. Therefore, the correct answer is 13.5 and 42.39.
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6.
If the diameter is 11.24 cm, find the radius _____ and the circumference _____ of the same circle.
Explanation The diameter of a circle is twice the length of its radius. Therefore, if the diameter is 11.24 cm, the radius would be half of that, which is 5.62 cm. The circumference of a circle can be calculated using the formula C = 2πr, where r is the radius. Plugging in the value of the radius (5.62 cm) into the formula, we get C = 2π(5.62) = 35.29 cm.
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7.
If the radius is 3.11 cm, find the diameter _____ and the circumference _____ of the same circle.
Explanation The diameter of a circle is twice the radius, so if the radius is 3.11 cm, the diameter would be 2 * 3.11 cm, which is equal to 6.22 cm. The circumference of a circle can be found using the formula C = 2πr, where r is the radius. Substituting the given radius of 3.11 cm into the formula, we get C = 2 * 3.14 * 3.11 cm, which is equal to 19.46 cm. Therefore, the correct answer is 6.36 and 19.97.
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8.
EIf the radius is 12.32 cm, find the diameter _____ and the circumference _____ of the same circle.
Explanation The correct answer is 24.64 and 77.37. The diameter of a circle is equal to twice the radius, so if the radius is 12.32 cm, the diameter would be 2 * 12.32 cm = 24.64 cm. The circumference of a circle is equal to 2 * π * radius, so if the radius is 12.32 cm, the circumference would be 2 * 3.14 * 12.32 cm = 77.37 cm.
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9.
If the diameter is 14.4 cm, find the radius _____ and the circumference _____ of the same circle.
Explanation The diameter of a circle is twice the length of its radius. Therefore, if the diameter is 14.4 cm, the radius would be half of that, which is 7.2 cm. The circumference of a circle can be found using the formula C = 2πr, where r is the radius. Plugging in the value of 7.2 cm for the radius, we get C = 2π(7.2) = 14.4π ≈ 45.22 cm.
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10.
If the radius is 1.84 cm, find the diameter _____ and the circumference _____ of the same circle.
Explanation The diameter of a circle is equal to twice the radius, so if the radius is 1.84 cm, the diameter would be 2 * 1.84 = 3.68 cm. The circumference of a circle can be found using the formula C = 2πr, where r is the radius. Plugging in the value of the radius (1.84 cm) into the formula, we get C = 2 * 3.14 * 1.84 = 11.56 cm. Therefore, the correct answer is 3.68 and 11.56.
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