In the next step of the derivation, we passed a horizontal plane through the sphere b up from the center. We let the radius of the cross section be x and formed a right triangle with hypotenuse r, as shown below.

The cross-sectional area of the shaded circle is πx2. Using the Pythagorean theorem for the right triangle, we get x2 + b2 = r2. Now solve for x2 and substitute it into the area expression.

What is the result?

π(r2 – b2)
π(r2 + b2)
π(b2 – r2)
2π(b2 + r2)

In 2000, for a certain region, 27.1% of incoming college freshman characterized their political views as liberal, 23.1% as moderate, and 49.8% as conservative. for this year, a random sample of 400 incoming college freshman yielded the frequency distribution for political views shown below. a. determine the mode of the data. b. decide whether it would be appropriate to use either the mean or the median as a measure of center. explain your answer. political view frequency liberal 118 moderate 98 conservative 184 a. choose the correct answer below. select all that apply. a. the mode is moderate. b. the mode is liberal. c. the mode is conservative. d. there is no mode.