CAST Domain 4: Mathematical Usage

A construction project requires 3.5 cubic yards of concrete per hour over an 8-hour workday. If concrete is ordered in cubic meters, how many cubic meters of concrete are needed for one day, given 1 cubic yard equals 0.764 cubic meters?

If the diameter of a cylindrical tank is increased by 20% and its height is reduced by 25%, what is the net effect on the tank's volume?

A worker is paid $15.50 per hour for a standard 40-hour week. For each hour over 40, the worker is paid 1.5 times the standard rate. If the worker works 50 hours in one week, what is their total weekly pay?

The area of a rectangular plot is 300 square meters. If the length is 5 times the width, what is the width of the plot in meters?

If a vehicle travels at an average speed of 45 miles per hour, how many miles will it travel in 15 minutes?

A contractor needs to distribute 600 bricks equally among 4 workers. After distribution, 2 more workers join. How many bricks must each of the original workers give to the new workers to ensure an equal share among all six workers?

The density of a material is 2.5 g/cm^3. What is the mass of a cube of this material with a side length of 4 cm?

If a circle has a circumference of 31.4 meters, what is its radius?

A construction project requires a concrete slab to be poured that is 30 feet long, 20 feet wide, and 0.5 feet thick. How many cubic yards of concrete are needed, given 1 cubic yard = 27 cubic feet?

A ladder leans against a wall at a height of 10 meters. If the bottom of the ladder is 6 meters from the base of the wall, what is the length of the ladder?

If the sum of three consecutive even numbers is 90, what is the smallest of these numbers?

A pipe carries water at a velocity of 3 meters per second. If the diameter of the pipe is doubled, what will be the new velocity of water in the pipe, assuming incompressible flow and conservation of mass?

A trapezoidal channel has a bottom width of 2 meters, a depth of 3 meters, and the side slopes are 1 vertical to 2 horizontal. What is the area of the cross-section in square meters?

The sum of the ages of three siblings is 42 years. If the youngest is half as old as the middle sibling, and the oldest is twice as old as the youngest, what is the age of the middle sibling?

A rectangular tank is 25% filled with water. After adding 750 liters of water, it is 50% full. What is the total capacity of the tank in liters?

A worker drives from Home to Work at a speed of 40 km/h and returns on the same route at 60 km/h. What is the average speed for the entire trip?

If 5 workers can complete a job in 8 days, how many days will it take 10 workers to complete the same job, assuming all workers work at the same rate?

A ladder leans against a wall forming a 60-degree angle with the ground. If the top of the ladder touches the wall 15 meters above the ground, what is the length of the ladder?

A train travels the first third of a distance at a speed of 30 km/h, the next third at 60 km/h, and the last third at 90 km/h. What is the average speed of the train over the entire distance?

A circular gear with a diameter of 0.5 meters is engaged with a smaller gear with a diameter of 0.2 meters. If the larger gear makes 10 revolutions per minute, how many revolutions per minute does the smaller gear make?