The volume of a cylinder can be found using the formula [tex]$V=\pi r^2 h$[/tex]. Which is the correct first step in finding the height of a cylinder with a volume of [tex]$192 \pi$[/tex] cubic inches and a radius of 5 inches?
A. [tex]$5=\pi(192)^2 h$[/tex]
B. [tex]$V=\pi+(5)^2+192 \pi$[/tex]
C. [tex]$V=\pi(5)^2(192)$[/tex]
D. [tex]$192 \pi=\pi(5)^2 h$[/tex]
Answer (2)
Substitute the given volume V = 192 π and radius r = 5 into the formula V = π r 2 h .
Obtain the equation 192 π = π ( 5 ) 2 h .
The correct first step is to substitute the values into the formula.
The resulting equation after substitution is 192 π = π ( 5 ) 2 h .
Explanation
Problem Analysis We are given the formula for the volume of a cylinder: V = π r 2 h , where V is the volume, r is the radius, and h is the height. We are given that the volume V = 192 π cubic inches and the radius r = 5 inches. We need to find the correct first step in finding the height h .
Substitution The first step is to substitute the given values into the formula. So, we replace V with 192 π and r with 5 in the formula V = π r 2 h . This gives us:
The equation after substitution 192 π = π ( 5 ) 2 h
Conclusion Therefore, the correct first step is to substitute the given values into the formula, which results in the equation 192 π = π ( 5 ) 2 h .
Examples
Understanding the volume of cylinders is crucial in many real-world applications. For instance, when designing cylindrical storage tanks for liquids or gases, engineers use the formula V = π r 2 h to determine the required dimensions to hold a specific volume. Similarly, in architecture, calculating the volume of cylindrical columns is essential for structural design and material estimation. Even in everyday scenarios like baking, knowing the volume of cylindrical cake pans helps in adjusting recipes and ensuring the cake fits perfectly. These examples highlight the practical importance of understanding and applying the formula for the volume of a cylinder.
The correct first step in finding the height of the cylinder is to substitute the given volume and radius into the volume formula, resulting in the equation 192 π = π ( 5 ) 2 h . Therefore, the answer is option D.
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