A tank is filled with gasoline to a depth of exactly 2 feet…
We are given that a tank, resting on its side, has gasoline filled to a depth of 2 feet. We are also given that the length of the tank, or the height of the cylinder, is 6 feet. We must determine the volume of the gas in the tank. Remember volume of a cylinder is πr^2h and we already are given that the height is 6 feet (i.e., h = 6).
Statement One Alone:
The inside of the tank is exactly 4 feet in diameter.
This means the radius of the circular ends is 2 feet (i.e., r = 2). Furthermore, using the information in statement one we know that the height of the tank while lying on its side is 4 feet. Because we know that the gasoline is at a depth of 2 feet, we know that the tank is half full of gas. Thus, the volume of the gas is:
½(π x 2^2 x 6)
½(π x 4 x 6)
We can eliminate choices B, C, and E.
Statement Two Alone:
The top surface of the gasoline forms a rectangle that has an area of 24 square feet.
We determine that the rectangle described in statement two would have dimensions made up of the height of the cylinder and the diameter of the circle. Since we know the height of the cylinder is 6, we can determine that the diameter of the circle is 4. Once again, knowing the length of the diameter is sufficient to answer the question.