Gas Tank Volume Calculation
How can we express the volume of a gas tank as a function of the radius r?
The volume of a gas tank with ends that are hemispheres of radius r feet and a cylindrical midsection that is 6 ft long can be expressed as a function of the radius r by calculating the volume of each component separately and then adding them together. 1. The two ends of the tank are hemispheres with a radius of r feet. The formula for the volume of a hemisphere is (2/3)πr^3. Since we have two hemispheres, we multiply this by 2 to get (4/3)πr^3. 2. The cylindrical midsection of the tank is 6 feet long. The formula for the volume of a cylinder is πr^2h, where r is the radius and h is the height. In this case, the height is 6 feet, and the radius is also r feet. So, the volume of the cylindrical midsection is 6πr^2. To find the total volume of the tank, we add the volume of the hemispheres to the volume of the cylindrical midsection: Total Volume = (4/3)πr^3 + 6πr^2 Therefore, the volume of the gas tank is expressed as a function of r as (4/3)πr^3 + 6πr^2. The unit of measurement for the volume will be in cubic feet due to working with feet as the unit for radius and length.