To obtain the total volume of ice cream, the following steps are necessary:
Step 1: Make a sketch of the shapes stated in the question, as below:
Step 2: Recall the formulas for the volume of a cone and that of a hemisphere, as follows:
The volume of a cone is:
And, the volume of a hemisphere is:
where, in both cases:
r = radius
h = perpendicular height
Step 3: Interpret the question to find clues, as follows:
"...that a half-scoop of ice cream is the shape of a hemisphere..." means that:
Thus, we have:
Since, the height of the cone is given to be 12 cm, we have:
Step 4: Now that we have used the clue to find the radius of the hemisphere (and cone), we can now proceed to find the total volume of the figure, as follows:
Thus:
Since:
h = 12 cm
r = 3cm
and pie = 3.14 (as given), we have that:
Therefore, the total volume of ice cream is 169.6 cubic centimeter