Question

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?

Answer 1

Answer:

1. If its radius is 2 inches, the height is 36 inches.

2. If its radius is 2 inches, the height is 16 inches.

3. If its radius is 2 inches, the height is 4 inches.

Step-by-step explanation:

Here is the complete question:

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

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 $h(r)$ of one of these cylinders is a function of its radius $r$, and

$h(r) =\frac{144}{r^{2} }$

Then, when r = 2 inches

$h(r) =\frac{144}{2^{2} }$

$h(r) =\frac{144}{4 }$

$h(r) = 36 inches$

Hence, the height is 36 inches

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

Again,

$h(r) =\frac{144}{r^{2} }$

Then, when r = 3 inches

$h(r) =\frac{144}{3^{2} }$

$h(r) =\frac{144}{9 }$

$h(r) = 16 inches$

Hence, the height is 16 inches

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

Again,

$h(r) =\frac{144}{r^{2} }$

Then, when r = 6 inches

$h(r) =\frac{144}{6^{2} }$

$h(r) =\frac{144}{36 }$

$h(r) = 4 inches$

Hence, the height is 4 inches.