Asurveyor wants to find the distance d across a river. using the measurements shown, what is a good estimate of d, in feet?

The easiest way to find the width of the river is to use the tangent function of a right triangle.  The base of your triangle is the 278 m that was measured along the river bank. The vertical side opposite the measured angle is the distance you are trying to find.

The tangent of an angle equals the opposite side divided by the adjacent side of the triangle.  Remember SOH CAH TOA?  Tangent = opposite/adjacent.

(a) the volume of the cone is 20/3 in3

hence, option a is correct.