Triangle abc is rotated to create the image a'b'c'.

which rule describes the transformation?

If you combine points A and A', B and B', C and C', you can see that all three lines are intersected at origin. This means that center of rotation is origin.

Now, in order to obtain point A' from point A, you have to rotate point A clockwise (or anti-clockwise) 180° about the origin; in order to obtain point B' from point B, you have to rotate point B clockwise (or anti-clockwise) 180° about the origin; in order to obtain point C' from point C, you have to rotate point C clockwise (or anti-clockwise) 180° about the origin.

That's why given rule rule describes the rotation by 180° clockwise (or anti-clockwise) about the origin.

A rotation of 180° about the origin

Step-by-step explanation:

To not the rule of rotation, you need to do the following:

1. Join A with A' and B with B'.

2. The point where the 2 lines meet is the center of rotation. Call this point X.

3. To know the angle of rotation, measure angle AXA' = BXB' = CXC'. This angle is 180°

Since the angle is a straight line, it does not matter whether it is clockwise or anticlockwise.

So the rule is "a rotation of 180° about the origin".

Draw a diagram to illustrate the problem as shown below.

Calculate the volume of the empty cone.
V₁ = (1/3)π*(6 in)²*(10 in) = 120π in³

Calculate the volume of the sphere.
V₂ = (4/3)π*(1.5 in)³ = 4.5π in³

The volume that can be filled with flavored ice is 
V = V₁ - V₂ = 115.5π in³ = 362.85 in³

Th volume is 115.5π in³ or 362.9 in³ (nearest tenth)