There are many cylinders with a volume of cubic inches. The height in inches of one of these cylinders is a function of its radius in inches where . What is the height of one of these cylinders if its radius is 2 inches? What is the height of one of these cylinders if its radius is 3 inches? What is the height of one of these cylinders if its radius is 6 inches?

There are many cylinders with a volume of 144[tex]\pi[/tex] cubic inches. The height [tex]h(r)[/tex] in inches of one of these cylinders is a function of its radius [tex]r[/tex] in inches where [tex]h(r) =\frac{144}{r^{2} }[/tex] .

1. What is the height of one of these cylinders if its radius is 2 inches?

2. What is the height of one of these cylinders if its radius is 3 inches?

3. What is the height of one of these cylinders if its radius is 6 inches?

Step-by-step explanation:

1. To determine the height of one of the cylinders if its radius is 2 inches,

From the question,

Since height [tex]h(r)[/tex] of one of these cylinders is a function of its radius [tex]r[/tex], and

[tex]h(r) =\frac{144}{r^{2} }[/tex]

Then, when r = 2 inches

[tex]h(r) =\frac{144}{2^{2} }[/tex]

[tex]h(r) =\frac{144}{4 }[/tex]

[tex]h(r) = 36 inches[/tex]

Hence, the height is 36 inches

2. To determine the height of one of the cylinders if its radius is 3 inches,

Again,

[tex]h(r) =\frac{144}{r^{2} }[/tex]

Then, when r = 3 inches

[tex]h(r) =\frac{144}{3^{2} }[/tex]

[tex]h(r) =\frac{144}{9 }[/tex]

[tex]h(r) = 16 inches[/tex]

Hence, the height is 16 inches

3. To determine the height of one of the cylinders if its radius is 6 inches,

Again,

[tex]h(r) =\frac{144}{r^{2} }[/tex]

Then, when r = 6 inches

[tex]h(r) =\frac{144}{6^{2} }[/tex]

[tex]h(r) =\frac{144}{36 }[/tex]

[tex]h(r) = 4 inches[/tex]

Hence, the height is 4 inches.