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How many pounds are in 192 ounces?
- A. 16 pounds
- B. 10 pounds
- C. 12 pounds
- D. 16 pounds
Correct Answer: C
Rationale: To convert ounces to pounds, divide the number of ounces by 16 since there are 16 ounces in a pound. Therefore, 192 ounces · 16 = 12 pounds. Choice A, 16 pounds, is incorrect because it does not represent the correct conversion from ounces to pounds. Choice B, 10 pounds, is incorrect as it is not the result of dividing 192 ounces by 16. Choice D, 16 pounds, is the same as choice A and is incorrect in the context of this conversion.
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How many pounds are in 176 ounces?
- A. 15 pounds
- B. 10 pounds
- C. 12 pounds
- D. 11 pounds
Correct Answer: D
Rationale: To convert ounces to pounds, you divide the number of ounces by 16 since there are 16 ounces in a pound. Therefore, 176 ounces · 16 = 11 pounds. Choice A is incorrect because it miscalculates the conversion. Choices B and C are also incorrect as they do not accurately convert the given ounces to pounds.
A circular bandage has a diameter of 6cm. What is the area covered by the bandage (area of a circle = πr^2)?
- A. 9π cm^2
- B. 18π cm^2
- C. 27π cm^2
- D. 36π cm^2
Correct Answer: C
Rationale: Rationale:
- The formula for the area of a circle is A = πr^2, where r is the radius of the circle.
- The diameter of the circular bandage is 6 cm, so the radius (r) is half of the diameter, which is 6/2 = 3 cm.
- Substitute the radius (r = 3 cm) into the formula for the area of a circle: A = π(3)^2 = 9π cm^2.
- Therefore, the area covered by the bandage is 9π cm^2.
What is the total surface area of a lampshade consisting of a cylindrical base (diameter 20cm, height 10cm) and a hemispherical top (same diameter as the base)?
- A. 785 sq cm
- B. 1130 sq cm
- C. 1570 sq cm
- D. 2055 sq cm
Correct Answer: D
Rationale: To find the total surface area of the lampshade, first calculate the surface area of the cylinder and the hemisphere separately.
1. Surface area of the cylinder = 2πr² + 2πrh = 2π(10)² + 2π(10)(20) = 400π + 400π = 800π cm².
2. Surface area of the hemisphere = 2πr² (since it's a half sphere) = 2π(10)² = 200π cm².
Adding both areas gives the total surface area: 800π + 200π = 1000π cm².
Now, calculate the numerical value: 1000π ≈ 3141.59 cm², which is approximately equal to 2055 cm². Therefore, the correct answer is 2055 sq cm.
Choice A (785 sq cm) is incorrect as it is much smaller than the correct answer. Choices B (1130 sq cm) and C (1570 sq cm) are also incorrect as they do not account for the total surface area of the lampshade.
Multiply: 3/4 1/3.
- A. 1/4
- B. 1/3
- C. 3/5
- D. 3/8
Correct Answer: A
Rationale: To multiply fractions, multiply the numerators together and the denominators together. In this case, 3/4 1/3 = (3 1) / (4 3) = 3/12 = 1/4. Therefore, the correct answer is A: 1/4. Choices B (1/3), C (3/5), and D (3/8) are incorrect because they do not result from the correct multiplication of the given fractions.
A train travels at a constant speed of 60 mph for 2 hours. How many miles did the train travel?
- A. 120 miles
- B. 180 miles
- C. 100 miles
- D. 240 miles
Correct Answer: A
Rationale: To determine the distance traveled by the train, you multiply the speed by the time: 60 mph 2 hours = 120 miles. Therefore, the correct answer is 120 miles. Choice B, 180 miles, is incorrect as it results from multiplying the speed by 3 hours instead of 2. Choice C, 100 miles, is incorrect as it results from multiplying the speed by 1.5 hours. Choice D, 240 miles, is incorrect as it results from multiplying the speed by 4 hours instead of 2.