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Module 1: Basic Concepts: Plane Geometry - Practice Problems


Instructions:: Work these problems on a sheet of paper and check your answers against those provided below.

#1: What is the area of a sphere having a diameter of 100 micrometers?

: Answer: 3.14 10^-4 cm²; Solution:

#2: What is the area of a cylinder excluding the circular top and bottom sections? Use a diameter of 6 in. and a height of 14 ft.

: Answer: 21.98 ft²; Solution:

#3: A pyramid hopper has a height of 10 ft, a width of 8 ft and a length of 8 ft. What is the capacity of the hopper if the density of solids in the hopper is 30 lb_m/ft³? Assume that the hopper is completely full.

: Answer: 6,400 lb_m; Solution:

Calculate the volume of the pyramid.
Calculate the capacity of the hopper.

#4: The gas flow rate leaving a stack is 189,000 actual ft³/min. What is the stack exit velocity in ft/min if the stack circular diameter at the discharge point is 9 ft?
See Figure 3. Use the following equation to work the problem:
Gas velocity = Gas flow rate/Area

: Answer: 2,973 ft/min; Solution:

Calculate the area of the circular stack at the
discharge point.
Calculate the stack exit velocity.

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