The cylindrical water tank on a semitrailer has a length of 20 feet. The volume of the tank is equal to the product of [tex]$\pi$[/tex], the square of the radius of the tank, and the length of the tank. Let [tex]$V$[/tex] represent the volume of the tank, [tex]$r$[/tex] represent the radius of the tank, and [tex]$h$[/tex] represent the length of the tank.
Part A: Create an equation that could be used to find the volume, [tex]$V$[/tex], of the cylindrical tank.
Answer (2)
The equation for the volume of the cylindrical tank is V = 20 π r 2 , where r is the radius. This is derived from the general formula for the volume of a cylinder, substituting the length with 20 feet. The volume determines how much liquid the tank can hold based on its radius.
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The volume of a cylinder is given by V = π r 2 h .
Substitute the given length h = 20 into the formula.
The equation for the volume of the cylindrical tank is V = 20 π r 2 .
The final equation is V = 20 π r 2 .
Explanation
State the formula for the volume of a cylinder and substitute the given length. The problem asks us to create an equation for the volume V of a cylindrical tank, given its radius r and length h . We know that the volume of a cylinder is given by the formula:
V = π r 2 h
We are also given that the length of the tank is 20 feet, so h = 20 . Substituting this value into the formula, we get:
V = π r 2 ( 20 )
V = 20 π r 2
Write the final equation. The equation that can be used to find the volume V of the cylindrical tank is:
V = 20 π r 2
Examples
Understanding the volume of a cylinder is useful in many real-world scenarios. For example, if you're designing a cylindrical storage tank for a chemical plant, you need to calculate its volume to ensure it can hold the required amount of liquid. The formula V = π r 2 h helps you determine the volume based on the tank's radius and height. Similarly, if you're calculating how much water a cylindrical pipe can carry, you'd use the same formula. Knowing the volume allows engineers to design efficient and safe systems.
