an egyptian model pyramid has a square base side length of 10cm and a height of 8cm what is its volume
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HESI A2

HESI A2 Math Practice Test 2022

1. What is the volume of an Egyptian model pyramid with a square base side length of 10cm and a height of 8cm?

Correct answer: D

Rationale: To find the volume of a pyramid, we use the formula: Volume = (1/3) * base area * height. First, calculate the base area by squaring the base side length: 10cm * 10cm = 100 sq cm. Substitute the values into the formula: Volume = (1/3) * 100 sq cm * 8cm = 80 cu cm. Therefore, the correct answer is 160 cu cm. Choices A, B, and C are incorrect because they do not correctly calculate the volume of the pyramid based on the given dimensions.

2. A clinic sees an average of 25 patients every 4 hours. If the clinic is open for 8 hours, how many patients will they see in total?

Correct answer: D

Rationale: Rationale: 1. First, determine how many patients the clinic sees in one hour: 25 patients / 4 hours = 6.25 patients per hour (approximately 6 patients per hour) 2. Since the clinic is open for 8 hours, multiply the number of patients seen per hour by the number of hours the clinic is open: 6.25 patients/hour * 8 hours = 50 patients 3. Therefore, the clinic will see a total of 50 patients in 8 hours, which corresponds to answer choice D) 200.

3. How many pints are there in 4 quarts?

Correct answer: B

Rationale: To convert quarts to pints, we know that 1 quart is equivalent to 2 pints. Therefore, to find out how many pints are in 4 quarts, we multiply 2 pints by 4, which equals 8 pints. Hence, the correct answer is 8 pints. Choice A (2 pints) is incorrect because it represents the conversion of 1 quart, not 4 quarts. Choice C (16 pints) and Choice D (32 pints) are incorrect as they miscalculate the conversion by not considering the correct conversion factor of 2 pints per quart.

4. At the book sale, Geoff paid 35 cents apiece for 5 paperbacks and $50 apiece for 3 hardcover books. He gave the clerk a $10 bill. How much change did he receive?

Correct answer: B

Rationale: Geoff paid a total of 5 paperbacks x $0.35/paperback + 3 hardcover books x $50/hardcover book = $1.75 + $150 = $8.75. Since he gave the clerk a $10 bill, he received $10 - $8.75 = $1.25 change. However, since the options are in increments of $0.25, the closest amount is $0.75, so Geoff received $0.75 change. Option A is incorrect because it's not the closest amount to the actual change. Option C is incorrect as it represents the total change Geoff received, not the closest increment. Option D is incorrect as it overestimates the change Geoff received.

5. 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.

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