ASVAB/AFQT Arithmetic Reasoning Practice Test 49: Geometry

Directions: In this test, you are tested on your ability to use arithmetic. Choose the best answer for each question.

1. The least angle of a triangle is 65 degrees less than the greatest angle. The third angle is 10 degrees greater than the least angle. What is the measure of the greatest angle?

2. One side of a square is doubled in length, and the adjacent side is tripled. The area of the resulting rectangle is 125 square centimeters greater than the area of the original square. How long is the rectangle's longest side?

3. Emil's mom, Bertha, wants him to build a rectangular garden in her backyard by walling off an area with planks. She wants it to cover an area of 162 square feet with an 18-foot border on at least one side. If the garden is 18 feet long, what is its width?

4. A triangle with an area of 100 square meters has a height that measures half as much as its base. What's the triangle's height?

5. Mason's Manholes Inc. needs to install a manhole cover over an open, circular pipe that has a diameter of 18 inches. If the manhole cover must have a -inch overlap all around, what is the manhole cover's surface area?

6. Sergeant First Class Aziz ordered his troops to fill four rectangular boxes with sand to hold down the flight line. If each box is 2.5 feet wide, 1 foot high, and 2 feet long, how many cubic feet of sand will the soldiers put into the boxes altogether?

7. An exterminator starts each day with a full canister of pesticide. If his 12-inch-tall cylindrical canister has a diameter of 10 inches, how many cubic inches of pesticide does it contain at the beginning of the exterminator's shift?

8. A can of soda has a diameter of 10 cm and a height of 15 cm. What is the volume of the soda in the can if 1 cm of space is left at the top of the can?

9. A triangle's longest side is four times the length of its shortest side, and its third side is 12 centimeters longer than the shortest side. The triangle's perimeter is 162 cm, so how long is its shortest side?

10. If one side of a square is increased by 6 cm and an adjacent side is decreased by 2 cm, a rectangle with a perimeter of 28 cm is formed. What is the area of the rectangle?

11. The smallest angle of a triangle has a measure that is 18 degrees less than the measure of the second angle, and the measure of the second angle is 33 degrees less than the measure of the greatest angle. What is the greatest angle's measurement?

12. Find the measure of ∠C in a triangle with measuring 38° and measuring 47°.

13. Specialists Vasquez and Wolley were told to sweep the company's motor pool. Vasquez started at 10 a.m. and swept a 50-foot by 50-foot portion of the motor pool, and Wolley began at 10:45 a.m. and swept the remainder of the motor pool, which was just as wide but 15 feet shorter than what Vasquez swept. What is the motor pool's total area?

14. Deedee needs to sweep her porch, which is 8 feet long and 12 feet wide. How many square feet will she have swept when she's finished with the entire porch?

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