Correct Answer: D

Rationale: To find the total surface area, we need to calculate the surface area of the cylindrical body and both hemispherical ends separately. The surface area of the cylinder is the sum of the lateral surface area (2πrh) and the area of the two circular bases (2πr^2). For the hemispheres, the surface area of one hemisphere is (2πr^2), so for two hemispheres, it would be (4πr^2). Given that the diameter of the cylinder and hemispherical ends is 10cm, the radius (r) is 5cm. Calculating the individual surface areas: Cylinder = 2π(5)(20) + 2π(5)^2 = 200π + 50π = 250π. Hemispheres = 4π(5)^2 = 100π. Adding these together gives a total surface area of 250π + 100π = 350π cm^2, which is approximately equal to 2055 sq cm. Therefore, the correct answer is D. Choice A (785 sq cm) is incorrect as it is significantly lower than the correct calculation. Choices B (1130 sq cm) and C (1570 sq cm) are also incorrect as they do not reflect the accurate surface area calculation for the given dimensions.

Correct Answer: C

Rationale: To convert quarts to gallons, remember that 1 gallon equals 4 quarts. Therefore, 16 quarts · 4 quarts/gallon = 4 gallons. The correct answer is 4 gallons because each gallon contains 4 quarts. Choice A (1 gallon) is incorrect because 1 gallon is equal to 4 quarts, not 16 quarts. Choice B (8 gallons) is incorrect as it miscalculates the conversion. Choice D (4.5 gallons) is incorrect because it doesn't align with the conversion rate of 4 quarts per gallon.

Correct Answer: D

Rationale: To find the total surface area, we need to calculate the surface area of the cylindrical body and both hemispherical ends separately. The surface area of the cylinder is the sum of the lateral surface area (2πrh) and the area of the two circular bases (2πr^2). For the hemispheres, the surface area of one hemisphere is (2πr^2), so for two hemispheres, it would be (4πr^2). Given that the diameter of the cylinder and hemispherical ends is 10cm, the radius (r) is 5cm. Calculating the individual surface areas: Cylinder = 2π(5)(20) + 2π(5)^2 = 200π + 50π = 250π. Hemispheres = 4π(5)^2 = 100π. Adding these together gives a total surface area of 250π + 100π = 350π cm^2, which is approximately equal to 2055 sq cm. Therefore, the correct answer is D. Choice A (785 sq cm) is incorrect as it is significantly lower than the correct calculation. Choices B (1130 sq cm) and C (1570 sq cm) are also incorrect as they do not reflect the accurate surface area calculation for the given dimensions.

Correct Answer: A

Rationale: The correct ratio of men to women is 3:4. To find the ratio, divide the number of men by the number of women: 12 men / 16 women = 3/4, which simplifies to 3:4. Therefore, in a class of 28 people with 12 men and 16 women, the ratio of men to women is 3:4. Choice B (4:7) is incorrect because it does not accurately reflect the given numbers of men and women in the class. Choice C (12:16) is incorrect as it represents the actual count of men and women, not the ratio. Choice D (1:2) is incorrect as it does not match the proportion of men to women in the class.

Correct Answer: B

Rationale: With y = 4 and x = 3, the expression is y x³. Substituting the values, we get 4 3³ = 4 27 = 108. Therefore, the correct answer is 108. Option A (-108) is incorrect because the negative sign is not part of the result. Option C (27) is incorrect as it only represents x³ without considering the value of y. Option D (4) is incorrect as it represents the initial value of y, not the result of y x³.