ITT Technical Institute
Framingham, Massachusetts
Quarter 2 CAD Mathematics
Instructor: Paul Burney

Name __________________________________

3-D Geometry--Volume and Surface Area (Test #4)


Please solve the following problems. Credit will be given for work completed so make sure to show it!


  1. Find the lateral surface area, total surface area, and volume of the following objects (20 points each)

    1. A sphere with a radius of 5 cm.

    2. A 2.5 inch tall triangular prism whose base is an equilateral triangle of side 0.75 inches.

    3. A frustum of a pyramid with a square top and bottom and measurements as listed below in the figure.

  2. The steel nut in the figure below has a diameter of 1.25". The side of the hexagonal hole in the center of the nut is 0.5".

    1. What is the volume of the nut?

    2. If steel weighs 0.2833 lb/cu in., what is the weight of the nut?

  3. The 30 m tall pyramid structure in front of the Louvre in Paris has a square base that is 75 m on each side. The slant height of the pyramid is 48 m long.

    1. What is the lateral surface area of the pyramid.

    2. If a protective coating costs 230 francs per square meter, how much would it cost to coat the outside of the pyramid?