a decorative box has a rectangular base 20cm by 15cm and a hemispherical top with the same diameter as the base what is the total surface area of the
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HESI A2

HESI A2 Math Practice

1. A decorative box has a rectangular base (20cm by 15cm) and a hemispherical top with the same diameter as the base. What is the total surface area of the box (excluding the base)?

Correct answer: C

Rationale: To find the total surface area of the box excluding the base, calculate the lateral surface area of the rectangular base and the surface area of the hemisphere. The lateral surface area of the rectangular base is 2(20cm x 15cm) = 600 sq cm. The surface area of the hemisphere is 2πr^2, where r is half the diameter of the base, so r = 10cm. Thus, the surface area of the hemisphere is 2π(10cm)^2 = 200π sq cm ≈ 628.32 sq cm. Add the lateral surface area of the base and the surface area of the hemisphere: 600 sq cm + 628.32 sq cm ≈ 1228.32 sq cm. Therefore, the total surface area of the box is approximately 1228.32 sq cm, which is closest to 1325 sq cm (Choice C). Choices A, B, and D are incorrect as they do not represent the accurate calculation of the total surface area of the box.

2. The nurse assisted the physician in removing the 'cast' from the patient's arm.

Correct answer: A

Rationale: The correct answer is A: 'Protective device.' A 'cast' is a hard protective device used to support and immobilize a broken bone. It is not a 'medicated sleeve' (B), a 'sling' (C), or a 'bandage' (D), as these items serve different purposes in medical care.

3. What does 'Excess' mean?

Correct answer: B

Rationale: The correct answer is B: 'More than what is needed or usual.' Excess refers to an amount that surpasses what is required or typical. Choice A is incorrect because 'less than what is needed or usual' is the opposite of excess. Choice C is incorrect as 'equal to the amount needed' does not imply excess. Choice D is incorrect as 'below average' does not capture the essence of excess.

4. Which of the following describes a vector quantity?

Correct answer: A

Rationale: A vector quantity is characterized by both magnitude and direction. In the provided options, choice A, '5 miles per hour due southwest,' fits this definition as it includes both the magnitude (5 miles per hour) and the direction (southwest), making it a vector quantity. Choices B and C only provide the magnitude without indicating any direction, hence they do not represent vector quantities.

5. How does the circulatory system work with the digestive system?

Correct answer: C

Rationale: The circulatory system works with the digestive system by transporting absorbed nutrients through the body. After digestion occurs in the digestive system, nutrients are absorbed into the bloodstream. The circulatory system then carries these nutrients to cells throughout the body where they are used for energy, growth, and repair. This process ensures that the necessary nutrients are delivered to where they are needed in the body. Choices A, B, and D are incorrect because the circulatory system is not responsible for removing undigested solids, filtering and collecting digested materials, or releasing enzymes that control digestion. These functions are primarily carried out by the digestive system.

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