Mathematics for Trades Flashcards

An electrician needs to run conduit at a 30° angle. If the horizontal run is 10 feet, what is the approximate length of conduit needed? (sin 30° = 0.5, cos 30° ≈ 0.866)

Answer: 11.55 ft

Conduit length = horizontal run / cos 30° = 10 / 0.866 ≈ 11.55 ft.

A welder needs to fill a cylindrical tank with a radius of 3 ft and a height of 5 ft. What is the volume? (π ≈ 3.14)

Answer: 141.3 cu ft

V = π × r² × h = 3.14 × 9 × 5 = 141.3 cu ft.

Bolt holes on a flange are spaced equally. If 8 holes are placed on a 12-inch diameter bolt circle, what is the center-to-center arc spacing in inches? (π ≈ 3.14)

Answer: 4.71 in

Circumference = π × 12 = 37.68 in; spacing = 37.68 / 8 = 4.71 in.

A piece of steel bar stock weighs 3.5 lbs per foot. An apprentice needs 7 pieces each 2.5 feet long. What is the total weight?

Answer: 61.25 lbs

Total length = 7 × 2.5 = 17.5 ft; weight = 17.5 × 3.5 = 61.25 lbs.

A roof has a 6:12 pitch (rise:run). If the horizontal run is 18 feet, what is the total rise?

Answer: 9 ft

Pitch 6:12 means 6 inches rise per 12 inches run; 6/12 × 18 ft = 9 ft rise.

A plumber orders pipe in 20-foot lengths. If a job requires 6 pieces at 3'8" each, how many full 20-foot lengths must be purchased?

Answer: 2

Each piece = 3 ft 8 in = 44 in = 3.667 ft; total = 6 × 3.667 = 22 ft; 2 lengths of 20 ft = 40 ft, which covers 22 ft — wait, 22 ft > 20 ft so 2 lengths needed.

A motor runs at 1,750 RPM and is connected via belt to a pulley with a 6-inch diameter. If the driven pulley has a 10-inch diameter, what is the driven speed?

Answer: 1,050 RPM

Driven RPM = (driver diameter / driven diameter) × driver RPM = (6/10) × 1,750 = 1,050 RPM.