Because the question wants arc length and gives you the measure of the central angle in radians, you can use the formula s = rθ to find the arc length: s = (8) ​\( \frac{5}{16}π \)​= ​\( \frac{40}{16}π \)​, which reduces to ​\( \frac{5}{2}π \)​, which is (B).

Tangent is defined as ​\( \frac{opposite}{adjacent} \)​. The side opposite angle XZY is 7, and the side adjacent to this angle is 8, so the tangent of ∠XYZ = ​\( \frac{7}{8} \)​, which is (C).

The trick is to recognize that DABC is a 30°-60°-90° right triangle. ∠ABC must equal 90° since a tangent line must be perpendicular to the radius of a circle drawn to the point of tangency. Only a 30°-60°-90° has a hypotenuse (AC) equal to double the length of one of the sides (AB). (You can also use the Pythagorean theorem to show this.) This means that ∠BAC = 60°, so the shaded region has a central angle measure of 360° – 60° = 300°. To get the area, use the proportion = ​\( \frac{Central Angle}{360°}=\frac{Sector Area}{Circle Area} \)​, or ​\( \frac{300°}{360°}=\frac{s}{21} \)​= . Reduce, cross-multiply, and solve to get s = 17.5. This matches (C).

For this question, you need to know that volume equals length × width × height. You know that the volume is 16,500, the depth (or height) is 10, and the length is 75. Just put those numbers in the formula: 16,500 = 75 × w × 10. Use your calculator to solve for w, which equals 22: (A).