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. What is the temperature in Celsius when it is 98.6 degrees Fahrenheit?

Correct answer: B

Rationale: To convert 98.6 degrees Fahrenheit to Celsius, you can use the formula (98.6 - 32) × 5/9. By solving this equation, the temperature is calculated to be 37°C. Therefore, the correct answer is B, 37 Celsius. Choice A, 35 Celsius, is incorrect because it is not the outcome of the conversion formula. Choice C, 38 Celsius, is incorrect as well, as it does not match the correct conversion result. Choice D, 36.5 Celsius, is also incorrect as it does not correspond to the accurate conversion from 98.6 degrees Fahrenheit.

3. If two workers can finish building a play set in 18 hours, how long will it take 4 workers to build 3 play sets?

Correct answer: A

Rationale: If 2 workers can complete building one play set in 18 hours, it means one worker would take 36 hours to complete the same task. When the number of workers is doubled to 4, the time is halved, so 4 workers would take 18 hours to build one play set. To build 3 play sets, the total time needed would be 3 times the time for one play set, which equals 54 hours. Therefore, 4 workers can build 3 play sets in 27 hours, making choice A the correct answer. Choices B, C, and D are incorrect because they do not account for the correct relationship between the number of workers and the time required to complete the task.

4. How many millimeters are in 4 meters?

Correct answer: B

Rationale: To convert meters to millimeters, you need to know that there are 1000 millimeters in 1 meter. Therefore, to find out how many millimeters are in 4 meters, you multiply 4 (meters) by 1000 (millimeters per meter), which equals 4000 millimeters. Choice A, 400 mm, is incorrect because it represents 4 decimeters, not 4 meters. Choice C, 40 mm, is incorrect because it represents 4 centimeters, not 4 meters. Choice D, 100 mm, is incorrect because it represents 1 meter, not 4 meters.

5. How many ounces are there in 4 cups?

Correct answer: A

Rationale: To find out how many ounces are in 4 cups, you need to multiply 8 ounces (the number of ounces in 1 cup) by 4 cups. This calculation results in 32 ounces. However, the question asks for the number of ounces in 4 cups, not the total ounces in 4 cups. Therefore, there are 16 ounces in 4 cups. Choices B, C, and D are incorrect as they do not represent the correct conversion of ounces in 4 cups.

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