1.16.7.b. Computation of volumes

Try these first

1. 1.

   What is the Trapezoidal Rule used for?

   Hint

   Think about how the areas are calculated.

2. 2.

   How would you define the Prismoidal Rule?

   Hint

   Focus on the shapes that it includes.

3. 3.

   What is the Trapezoidal Rule used to calculate?

   • Area
   • Volume
   • Length

   Hint

   Think about why we need to use averages in calculations.

4. 4.

   True or False: The Prismoidal Rule is only applicable to parallel bases.

   • True
   • False

   Hint

   Consider the physical characteristics of prismoids.

5. 5.

   Given the length between two cross-sections is 12 m, and areas of cross-sections are 70 m² and 50 m², calculate the volume using the Trapezoidal Rule and state the method clearly.

   Hint

   Revisit how we averaged the areas and applied the length.

6. 6.

   A prismoid has cross-sectional areas of 30 m², 70 m², and 50 m² over a distance of 15 m. Compute the volume using the Prismoidal Rule and explain your reasoning.

   Hint

   Ensure you apply each section's area properly according to the formula.