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A right circular cylinder has a height of 19 3/4 …

Mathematics Questions

A right Circular cylinder has a height of 19 3/4 ft and a diameter 1 2/5 times its height . What is the volume of the cylinder?

Short Answer

To calculate the volume of a cylinder, first gather the height (19.75 ft) and diameter (27.65 ft) using the formula Diameter = 1.4 √o Height. Then, find the radius (13.825 ft) and apply the volume formula V = œAr¬≤h, resulting in a volume of 11,852.9 ft¬≥.

Step-by-Step Solution

Step 1: Gather Cylinder Measurements

To calculate the volume of a cylinder, start by collecting essential measurements: the height and diameter. In this case, the height of the cylinder is given as 19.75 ft. The diameter is calculated using the formula: Diameter = 1.4 ‚àöo Height, which results in a diameter of 27.65 ft.

Step 2: Calculate the Radius

The next step is to find the radius of the cylinder, which is half of the diameter. Use the formula: Radius = Diameter / 2. For our calculations, this gives us a radius of 13.825 ft. Make sure to keep the measurements precise for accurate volume calculation.

Step 3: Apply the Volume Formula

Now that you have the height and radius, insert these values into the volume formula for a cylinder: V = œAr¬≤h. Substituting the values, you calculate: V = 3.14 √o (13.825)¬≤ √o 19.75, which results in a volume of 11,852.9 ft¬≥. This formula provides the total capacity of the cylinder.

Related Concepts

Height

The vertical measurement of the cylinder, which determines how tall it is from the base to the top.

Diameter

The distance across the circular base of the cylinder, measured through the center, and is used to calculate the radius.

Radius

The distance from the center of the circular base to its edge, which is half of the diameter and is used in calculating the volume of the cylinder.