GED and HiSET mathematics — surface area, volume and scale

The GED Mathematical Reasoning test prints a formula sheet with the surface area and volume of a rectangular prism, a right prism, a cylinder, a pyramid, a cone and a sphere, and the HiSET Mathematics test asks measurement and geometry questions of the same kind. Having the formula in front of you only helps if you can tell which one fits the object, what each letter stands for, and whether the question wants the outside of a shape or the space inside it. This material trains those choices on objects adults actually handle: shipping boxes, cans, tanks, gravel, silos and floor plans.

The twelve quiz questions cover every solid on the sheet. You find the surface area of a shipping box and the full surface area of a can with both lids, then the area of only the curved side of a water tank, the part a painter actually covers. You compute the volume of a cone-shaped pile of gravel, a spherical propane tank, a square pyramid and a triangular prism, and the volume of a grain silo built from a cylinder and a half sphere. You work backward from the 628 cubic feet a tank must hold to the height it needs. Three questions are about scale: a real wall length from a floor plan drawn at a quarter inch to the foot, the area of a yard when every length on a plan is doubled, and the real volume of a storage unit built as a 1:10 model.

The wrong options are the numbers that common slips produce: the cone without its one third, the diameter used as the radius, a radius not squared, both lids added when only the side is painted, a whole sphere where half belongs, and the scale factor squared where it should be cubed. The explanation after each answer says which slip leads to which number.

The flashcards list the surface-area and volume formulas, the lateral area of a cylinder, the meaning of B as the area of the base, and how a scale factor changes lengths, areas and volumes.

The written work asks for complete solutions on paper, with units: the surface area of a cone and of a pyramid, a sphere's volume, a composite building, a missing dimension, and scale-drawing and scale-factor problems. The oral exam asks one question at a time and expects you to say which formula you chose and why.

The material is independent practice written by Zestly, based on the published content of the GED and HiSET mathematics tests; it is not produced or endorsed by GED Testing Service or ETS.

• Choose between surface area, lateral area and volume from the wording of a problem
• Compute surface area of rectangular prisms, cylinders, cones and pyramids
• Compute volume of prisms, cylinders, pyramids, cones and spheres, using 3.14 for pi
• Find the volume of a composite solid by adding its parts
• Solve a volume formula for a missing dimension
• Use a drawing scale to find real lengths and explain how a scale factor k changes area (k squared) and volume (k cubed)

Practice material written by Zestly, based on the published content of the GED Mathematical Reasoning test (geometry and measurement; surface area and volume formulas as printed on the GED Mathematics Formula Sheet, GED Testing Service, 2014 test: rectangular prism, right prism, cylinder, pyramid, cone, sphere, pi approximately 3.14) and the HiSET Mathematics test (measurement and geometry).