a bookshelf has triangular shelves with a base of 40cm and a height of 30cm the depth of the shelf is 25cm what is the volume of each shelf

HESI A2

Practice HESI A2 Math Test

1. A bookshelf has triangular shelves with a base of 40cm and a height of 30cm. The depth of the shelf is 25cm. What is the volume of each shelf?

A. 3000 cu cm
B. 3750 cu cm
C. 5000 cu cm
D. 7500 cu cm

Correct answer: B

Rationale: To find the volume of the triangular shelf, first calculate the area of the triangle (1/2 * base * height) which is (1/2 * 40 * 30) = 600 sq cm. Then, multiply this area by the depth of the shelf (600 * 25) = 15000 cu cm. Therefore, the volume of each shelf is 3750 cu cm. Choice A, C, and D are incorrect as they do not correctly calculate the volume based on the dimensions provided.

2. A train travels at 65 mph for 1.5 hours. How far did it travel?

A. 97.5 miles
B. 95 miles
C. 100 miles
D. 100.5 miles

Correct answer: A

Rationale: To find the distance traveled, multiply the speed of the train (65 mph) by the time it traveled (1.5 hours): 65 mph × 1.5 hours = 97.5 miles. Therefore, the train traveled 97.5 miles. Choice B, 95 miles, is incorrect as it does not account for the correct calculation. Choice C, 100 miles, is incorrect as it is a rounded-up value. Choice D, 100.5 miles, is incorrect as it is a miscalculation.

3. A birdbath has a hemispherical bowl with a diameter of 30cm. What is its volume?

A. 675 cu cm
B. 1350 cu cm
C. 2700 cu cm
D. 4050 cu cm

Correct answer: C

Rationale: To find the volume of a hemispherical bowl, we use half the formula for a sphere's volume: (2/3) * π * (radius)^3. Given the diameter is 30cm, the radius is half of that, which is 15cm. Substitute the radius into the formula: (2/3) * π * (15cm)^3 ≈ 2700 cu cm. Therefore, the correct volume is approximately 2700 cu cm. Choices A, B, and D are incorrect as they do not correctly calculate the volume of the hemispherical bowl.

4. After taking several practice tests, Brian improved the results of his GRE test by 30%. Given that the first time he took the test Brian answered 150 questions correctly, how many questions did he answer correctly on the second test?

A. 105
B. 120
C. 180
D. 195

Correct answer: D

Rationale: If Brian answered 150 questions correctly on the first test, after improving his results by 30%, he would have answered (150 * 1.30) = 195 questions correctly on the second test. Therefore, the correct answer is 195, option D. Choices A, B, and C are incorrect as they do not account for the 30% improvement in the number of questions Brian answered correctly on the second test.

5. What is the perimeter of a garden bed with a side length of 8 meters?

A. 16m
B. 24m
C. 32m
D. 64m

Correct answer: B

Rationale: The correct answer is B: 24m. The perimeter of a square is found by adding up all its sides. In this case, since the garden bed has a side length of 8 meters, the perimeter would be 8m + 8m + 8m + 8m = 24m. Choices A, C, and D are incorrect because they do not correctly calculate the perimeter of a square with a side length of 8 meters.