Agronomy Degree Practice Exam

How many bushels can a grain bin with a 30-foot diameter and 35 feet tall hold if filled to the top, using π (pi) as 3.14?

1. 20,606.3 bushels

2. 25,000 bushels

3. 18,000 bushels

4. 22,500 bushels

The correct answer is: 20,606.3 bushels

To determine the capacity of the grain bin in bushels, we first need to calculate the volume of the cylinder. The formula for the volume \( V \) of a cylinder is: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height. In this case, the diameter of the bin is 30 feet, so the radius \( r \) is half of that, which is 15 feet. The height \( h \) is given as 35 feet. Using \( \pi \) as 3.14, we can plug in the values: 1. Calculate the area of the base: \[ r^2 = 15^2 = 225 \text{ square feet} \] 2. Now calculate the volume: \[ V = 3.14 \times 225 \times 35 \] First, calculate \( 3.14 \times 225 \): \[ 3.14 \times 225 = 706.5 \text{ square feet} \] Then multiply by the height: \[ V = 706.5