Session 8, Part B:
Volume Formulas (60 minutes)

In This Part: Cross Section Method | Cylinders, Cones, and Spheres

 In Part A we found that we can determine the volume of rectangular prisms or boxes by multiplying the dimensions (length • width • height). Another way to determine the volume is to find the area of the base of the prism and multiply the area of the base by the height. This second method is sometimes referred to as the cross-section method and is a useful approach to finding the volume of other figures with parallel and congruent cross sections, such as triangular prisms and cylinders. Notice in the figures above that each cross section is congruent to a base. Note 3 Problem B1 The formula for the volume of prisms is V = A • h, where A is the area of the base of the prism, and h is the height of the prism. Does it matter which face is the base in each of the following solids? Explain.

 Problem B2 Find the volume of the figures above using the cross-section method.

 Problem B3 How do we go about finding the volume of a figure that is not a prism-like solid? The figure below has two bases, and every cross section of the solid is a circular region that is parallel to a base. The circular cross sections, however, are not all congruent. To find the exact volume of this solid involves using methods from calculus, but can you find an approximate volume with the information about the cross sections indicated here? Find the approximate volume of the prism-like vase above, given the areas of some of its cross sections.

 Session 8: Index | Notes | Solutions | Video

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