HESI A2
HESI A2 Math
1. A water fountain has a spherical base with a diameter of 50cm and a cylindrical body with a diameter of 30cm and a height of 80cm. What is the total surface area of the fountain (excluding the water surface)?
- A. 3142 sq cm
- B. 4712 sq cm
- C. 5486 sq cm
- D. 7957 sq cm
Correct answer: C
Rationale: To find the total surface area of the fountain, we first calculate the surface area of the sphere and the cylinder separately. For the sphere: - Radius = Diameter / 2 = 50 / 2 = 25 cm - Surface area of a sphere = 4πr² = 4 x π x 25² = 500π cm² For the cylinder: - Radius = Diameter / 2 = 30 / 2 = 15 cm - Surface area of a cylinder = 2πrh + 2πr² = 2 x π x 15 x 80 + 2 x π x 15² = 240π + 450π = 690π cm² Total surface area = Surface area of sphere + Surface area of cylinder = 500π + 690π = 1190π cm² ≈ 5486 sq cm. Therefore, the correct answer is C. Choice A (3142 sq cm) is incorrect as it is much smaller than the correct answer. Choices B and D are also incorrect as they do not reflect the accurate calculation of the total surface area of the fountain.
2. How many liters are in 2500 milliliters?
- A. 2.5 liters
- B. 1.5 liters
- C. 3.5 liters
- D. 0.25 liters
Correct answer: A
Rationale: The correct answer is A: 2.5 liters. There are 1,000 milliliters in a liter. To convert 2,500 milliliters to liters, you need to divide by 1,000: 2,500 / 1,000 = 2.5 liters. Choice B (1.5 liters) is incorrect because it miscalculates the conversion. Choice C (3.5 liters) is incorrect as it overestimates the conversion. Choice D (0.25 liters) is incorrect as it underestimates the conversion. Therefore, the correct conversion is 2.5 liters.
3. Change 0.004 to a ratio.
- A. 1:250
- B. 17:40
- C. 9:20
- D. 20:40
Correct answer: A
Rationale: To convert 0.004 to a ratio, first express it as a fraction. 0.004 = 4/1000 = 1/250. Therefore, the ratio is 1:250. Choice A is the correct answer. Choices B, C, and D are incorrect ratios as they do not represent the equivalent fraction of 0.004.
4. An architect is designing a rectangular room. The room has an area of 225 square feet and a width of 15 feet. What is the length of the room?
- A. 30 feet
- B. 15 feet
- C. 25 feet
- D. 45 feet
Correct answer: B
Rationale: The formula for the area of a rectangle is: Area = Length × Width. To find the length, divide the area by the width: 225 ÷ 15 = 15 feet. Therefore, the correct answer is 15 feet. Choice A (30 feet) is incorrect because it is the product of the area and the width, not the length. Choice C (25 feet) is incorrect as it does not match the result of dividing the area by the width. Choice D (45 feet) is incorrect as it is not the result of the calculation needed to find the length.
5. Which number system is commonly used in the United States?
- A. Tertiary
- B. Decimal
- C. Napoleonic
- D. Binary
Correct answer: B
Rationale: The correct answer is B: Decimal. The decimal system, also known as the base-10 system, is the standard system for denoting integer and non-integer numbers in the United States and many other countries. In the decimal system, numbers are represented using 10 digits (0-9). Choices A, C, and D are incorrect. Tertiary, Napoleonic, and Binary number systems are not commonly used for general number representation in the United States.
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