CAST Domain 1: Graphic Arithmetic

If a blueprint has a scale of 1 inch equals 30 feet, and a room on the blueprint is 4 inches by 6 inches, what is the actual size of the room in feet?

A cylindrical tank's blueprint shows a diameter of 2 inches and a height of 3 inches. If the scale is 1 inch = 5 feet, what is the actual volume of the tank in cubic feet?

A floor plan shows a rectangular swimming pool that is 3 inches long and 2 inches wide on the blueprint. If the scale is 1 inch = 10 feet, what is the area of the actual swimming pool in square feet?

On a site plan, a landscaped area is represented by a circle with a diameter of 4 inches. If the scale is 1 inch = 20 feet, what is the actual area of the landscaped area in square feet?

A scale model of a bridge span is 8 inches long and represents an actual span of 240 feet. If the height of the model bridge is 1 inch, what is the actual height of the bridge?

An engineering drawing shows a pipeline that runs diagonally across a square piece of land, from one corner to the opposite corner. If the side of the square is 3 inches on the drawing and the scale is 1 inch = 40 feet, what is the actual length of the pipeline?

A map includes a rectangular parking lot that measures 2 inches by 3 inches. With a scale of 1 inch = 50 feet, what is the perimeter of the actual parking lot?

If a construction plan shows an equilateral triangle with each side measuring 2 inches and the scale is 1 inch = 25 feet, what is the actual perimeter of the triangular area?

A site plan shows a circular garden with a radius of 1.5 inches. If the scale is 1 inch = 10 feet, what is the circumference of the actual garden in feet?

In a plan drawing, a rectangular reservoir is 5 inches long and 2 inches wide. If the scale is 1 inch = 20 feet, what is the actual volume of the reservoir if its depth is 10 feet?

A landscaping design includes a path that runs from the northwest corner of a square park to the southeast corner. If each side of the park measures 4 inches on the plan, and the scale is 1 inch = 15 feet, what is the actual length of the path?

A blueprint shows a pentagonal room where each side is 1.5 inches long. If the scale is 1 inch = 40 feet, what is the perimeter of the actual room in feet?

An architectural drawing includes an elliptical garden with major axis 4 inches and minor axis 2 inches on the blueprint. If the scale is 1 inch = 10 feet, what is the area of the actual garden in square feet?

A site plan shows a spiral staircase that makes exactly 5 rotations with each rotation rising 2 feet. If the scale is 1 inch = 5 feet, and the diameter of the staircase is 3 inches on the drawing, what is the total vertical height gained by the staircase?

A construction plan shows a hexagonal window with sides of 2 inches each. If the scale is 1 inch = 6 feet, what is the total length of the frame needed to go around the window in feet?

On a landscaping blueprint, a circular flower bed has a circumference of 3.14 inches. If the scale is 1 inch = 20 feet, what is the diameter of the actual flower bed in feet?

A development plan features a walking path that follows the outer edge of a sector of a circle. The sector has a central angle of 60 degrees and a radius of 3 inches on the plan. If the scale is 1 inch = 30 feet, what is the length of the walking path along the sector's arc in feet?

An irrigation layout includes a parabolic arc for water trajectory, starting and ending at the same height with a maximum height of 4 inches above the starting height at the midpoint. If the scale is 1 inch = 5 feet, and the distance between the start and end points is 8 inches on the drawing, what is the actual maximum height of the water trajectory?

A detailed architectural rendering shows an octagonal gazebo with each side measuring 1 inch on the blueprint. If the scale is 1 inch = 12 feet, how much fencing is required to enclose the gazebo perimeter in feet?

In a construction schematic, a trapezoidal water channel has bases of 2 inches and 3 inches and a height of 1 inch on the drawing. If the scale is 1 inch = 25 feet, what is the area of the actual water channel in square feet?