Question

This is an EXPLAIN YOUR THOUGHTS question. Be sure to answer ALL parts of the questions and include all your work!

Task: Find the volume of the figure below. (Hint: divide them into two figures you know how to solve for).

Part a) What is your strategy, ie what shapes can you divide the figure into to find the volume?

Part b) What eqautions will you use to find the VOLUME? First state the general equations. Then include the known values into the equation.

Part c) What is the VOLUME? (don't forget units!)

Answer 1

a) The figure can be reasonably divided into two geometries:
• a rectangular prism
• a hemisphere.

b) The volume of the rectangular prism is given by
V = lwh
V = (10 cm)(5 cm)(4 cm) = 200 cm³

The volume of the hemisphere is given by
V = (2π/3)r³
V = (2π/3)(3 cm)³ = 18π cm³

c) The total volume of the figure is
total volume = (prism volume) + (hemisphere volume)
V = 200 cm³ + 18π cm³
V ≈ 256.549 cm³