Answer: To determine whether the water from the cylindrical water tank will fit into the rectangular trough or overflow, we need to compare the volumes of the tank and the trough.
First, let's calculate the volume of the cylindrical water tank. The formula for the volume of a cylinder is:
Volume = π * r^2 * h
where π is approximately 3.14, r is the radius (half the diameter), and h is the height.
Given that the diameter of the tank is 2 m, the radius is 2 / 2 = 1 m, and the height is 15 m.
Volume of the tank = 3.14 * (1^2) * 15
Volume of the tank ≈ 47.1 m^3
Now, let's calculate the volume of the rectangular trough. The formula for the volume of a rectangular box is:
Volume = length * width * height
Given that the length of the trough is 13 m, the width is 0.9 m, and the height is 0.45 m.
Volume of the trough = 13 * 0.9 * 0.45
Volume of the trough ≈ 5.445 m^3
Since the volume of the tank (47.1 m^3) is significantly larger than the volume of the trough (5.445 m^3), we can conclude that the water from the tank will not fit into the trough. It will overflow.
Explanation: