a pressure vessel has a cylindrical body diameter 10cm height 20cm with hemispherical ends same diameter as the cylinder what is its total surface are
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HESI A2

HESI A2 Quizlet Math

1. A pressure vessel has a cylindrical body (diameter 10cm, height 20cm) with hemispherical ends (same diameter as the cylinder). What is its total surface area?

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.

2. Gerald can bake 3 dozen cookies in 30 minutes. How long will it take him to bake 12 dozen cookies?

Correct answer: B

Rationale: If Gerald can bake 3 dozen cookies in 30 minutes, then he can bake 1 dozen cookies in 10 minutes (30 minutes / 3 = 10 minutes). To bake 12 dozen cookies, it would take him 120 minutes (12 dozen x 10 minutes = 120 minutes), which is equivalent to 1 hour and 40 minutes. Choice A (90 minutes) is incorrect because it does not account for the correct proportion of cookies baked. Choice C (2 hours) and Choice D (4 hours) are incorrect as they overestimate the time required based on the given information.

3. There are 6,657 marbles in a jar. Approximately 34% are white, and the rest are black. How many black marbles are there?

Correct answer: A

Rationale: To find the number of black marbles, we need to calculate the percentage that represents the black marbles, which is 100% - 34% = 66%. Then, we find 66% of 6,657 to determine the number of black marbles. 66% of 6,657 is approximately 4,394, so there are 4,394 black marbles in the jar. Choice A is correct. Choices B, C, and D are incorrect as they do not reflect the correct calculation for the number of black marbles in the jar.

4. 25 1/7 - 12 5/7 = ?

Correct answer: A

Rationale: To subtract mixed numbers, subtract the whole numbers and fractions separately. If necessary, borrow from the whole number when the fraction in the minuend is smaller than the fraction in the subtrahend. The whole numbers are: 25 - 12 = 13. The fractions: 1/7 - 5/7. Since 1/7 is smaller, borrow 1 from 13, making it 12. Then convert 1 whole into 7/7, so the fraction becomes: (7/7 + 1/7) - 5/7 = 8/7 - 5/7 = 3/7. Thus, 25 1/7 - 12 5/7 = 12 3/7.

5. A nurse works in a neonatal unit where infants' weights are measured in grams. What is the equivalent of 1,500 grams in pounds?

Correct answer: A

Rationale: To convert grams to pounds, you can use the conversion factor: 1 pound = 453.59237 grams. Therefore, to find the equivalent of 1,500 grams in pounds, divide 1,500 by 453.59237 to get approximately 3.3 pounds. Choice A is the correct answer because it accurately represents the conversion. Choices B, C, and D are duplicates and do not provide an alternative option.

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