standard_description: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
problem_activity: A tank that measures
$$1\frac{1}{2}$$
feet across,
$$2\frac{1}{3}$$
feet wide, and
$$1\frac{1}{2}$$
feet tall, is filled halfway with water, as shown below. To fill the tank to the very top with water, how many cubic feet of water need to be added?
[IMG]


aligns: no