Geometric problems on the ASVAB require you to compute the volume, perimeter, area, circumference, diameter, and so on of various geometric shapes. These problems are not very difficult with a little knowledge of some geometric formulas.
You’re painting a fence that is 20 feet long and 6 feet high. How much square footage of fence are you covering with paint?
The area formula for a rectangle is a = lw, so the answer to this simple problem is a = 6 × 20 = 120 square feet.
Generally, the Arithmetic Reasoning test makers don’t let you off so easy, though. The problem is more likely to be written something like the following.
You’re painting a fence that is 20 feet long and 6 feet high. Paint costs $7.23 per gallon, and 1 gallon of paint covers 60 square feet of fence. How much do you need to spend on paint to complete the project?
The problem now requires a couple of extra steps to answer. First, you have to compute the area of the fence. You already did that: 120 square feet.
Now you have to determine how many gallons of paint you need to buy to cover 120 square feet. Because 1 gallon of paint covers 60 square feet, you need 120 ÷ 60 = 2 gallons of paint.
Finally, you need to figure how much 2 gallons of paint cost. Paint is $7.23 per gallon, and you need 2 gallons, so $7.23 × 2 = $14.46.
You get quite a few geometric problems on the Arithmetic Reasoning subtest. To make sure you’re ready for them, memorize these basic geometric formulas.
Shape | Function | Formula |
---|---|---|
Square | Area | a = s2 |
Perimeter | p = 4s | |
Rectangle | Area | a = lw |
Perimeter | p = 2l + 2w | |
Triangle | Perimeter | p = s1 + s2 + s3 |
Area | a=1/2bh | |
Right Triangle | Pythagorean theorem | a2 + b2 = c2 |
Circle | Radius | r=1/2d |
Diameter | d = 2r | |
Circumference | c = 2ðr | |
Area | a = ðr2 | |
Cube | Volume | v = s3 |
Surface Area | SA = 6s2 | |
Rectangular Box | Volume | v = lwh |
Surface Area | SA = 2lw + 2wh + 2lh | |
Cylinder | Volume | v = ðr2h |