Free ASVAB Practice Tests

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(4²) + 2π(4 x 5)
sa = 2π(16) + 2π(20)
sa = (2 x 16)π + (2 x 20)π
sa = 32π + 40π
sa = 72π

The mechanical advantage of a wheel and axle is the input radius divided by the output radius:

MA = \( \frac{r_i}{r_o} \)

In this case, the input radius (where the effort force is being applied) is 4 and the output radius (where the resistance is being applied) is 3 for a mechanical advantage of \( \frac{4}{3} \) = 1.33

MA = \( \frac{load}{effort} \) so effort = \( \frac{load}{MA} \) = \( \frac{35 lbs.}{1.33} \) = 26.32 lbs.

A fixed pulley is used to change the direction of a force and does not multiply the force applied. As such, it has a mechanical advantage of one. The benefit of a fixed pulley is that it can allow the force to be applied at a more convenient angle, for example, pulling downward or horizontally to lift an object instead of upward.

The ripsaw delivers maximum efficiency at cutting with or along the grain (ripping).

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Calipers are similar to micrometers in shape but instead of measuring distances, calipers are used to transfer distances between objects. An outside caliper is used to transfer outside dimensions while an inside caliper is used to transfer inside distances. A vernier caliper is an extremely precise caliper (down to \({1 \over 1000}\) inch) that allows measuring / transferring either inside or outside dimensions.

Primary consumers (herbivores) subsist on producers like plants and fungus.  Examples are grasshoppers, cows, and plankton.

To balance this lever the torques at the green box and the blue arrow must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

Solving for R_a, our missing value, and plugging in our variables yields:

R_a = \( \frac{R_bd_b}{d_a} \) = \( \frac{15 lbs. \times 8 ft.}{7 ft.} \) = \( \frac{120 ft⋅lb}{7 ft.} \) = 17.14 lbs.

Rulers are used to both measure distance and to draw straight lines. Tape measures are flexible rulers made from cloth or metal and are useful for measuring longer distances and in tighter spaces. Both rulers and tape measures provide similar accuracy, commonly down to \({1 \over 16}\) or \({1 \over 32}\) inch. A steel framing square is made up of a shorter ruler (tongue) and a longer ruler (blade) that meet at a 90° (right) angle. A framing square is often used by carpenters when framing stairs and roofs.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{75mi}{25mph} \)
3 hours