a lampshade consists of a cylindrical base diameter 20cm height 10cm and a hemispherical top same diameter as the base what is its total surface area
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HESI A2

HESI A2 Math Practice

1. 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)?

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.

2. If his distribution cost is $10, what will be his profit?

Correct answer: B

Rationale: To calculate profit, we subtract the total distribution cost from the revenue. Given that the revenue is $30, the calculation is as follows: Profit = Revenue - Distribution Cost. Therefore, Profit = $30 - $10 = $20. Hence, the profit will be $19.60. Choice A is incorrect as it incorrectly adds the distribution cost to the revenue. Choice C is incorrect as it does not consider the distribution cost. Choice D is incorrect as it overestimates the profit by adding the distribution cost again to the correct profit amount.

3. A female ran a 24-mile course. Her first 6 miles she ran in 1 hour. The second set of 6 miles in 1.2 hours. The third set of 6 miles in 1.5 hours. The fourth set of 6 miles in 1.6 hours. How long did it take her to complete the course?

Correct answer: B

Rationale: To find the total time, add the times for each set of 6 miles: 1 + 1.2 + 1.5 + 1.6 = 5.3 hours. Therefore, it took her 5.3 hours to complete the 24-mile course. Choice A, 5 hours, is incorrect because the total time is slightly more than that. Choice C, 4 hours, is incorrect as it doesn't account for the total time taken. Choice D, 6 hours, is incorrect as it's an overestimation of the actual time taken.

4. The physician orders 1000 mg of Benadryl liquid; 1 g = 1 tsp. How many teaspoons will you give?

Correct answer: C

Rationale: Since 1 gram (g) equals 1000 milligrams (mg) and 1 g = 1 teaspoon (tsp), the prescribed 1000 mg is equal to 1 tsp. Therefore, you will give 1 teaspoon of the Benadryl liquid. Choices A, B, and D are incorrect because they do not correspond to the correct conversion of 1 g to 1 tsp, which is essential in solving this dosage calculation.

5. Multiply 12 by 15 and express the result as a decimal:

Correct answer: D

Rationale: To find the product of 12 and 15, you simply multiply them together. 12 multiplied by 15 equals 180. To express 180 as a decimal, you divide by 100. Therefore, the correct answer is 1.8. Choices A, B, and C are incorrect as they represent values that are not the correct result of multiplying 12 by 15 and converting it to a decimal.

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