Answered

The volume of a right circular cylinder can be approximated using the formula:

[tex]\[ \text{Volume} = \pi r^2 h \][/tex]

where [tex]\( r \)[/tex] is the radius of the cylinder and [tex]\( h \)[/tex] is the height of the cylinder. Using this formula, calculate the volume of a right circular cylinder with a radius of 3 meters and a height of 5 meters.

A. [tex]\( 405 \, \text{m}^3 \)[/tex]
B. [tex]\( 2,025 \, \text{m}^3 \)[/tex]
C. [tex]\( 675 \, \text{m}^3 \)[/tex]
D. [tex]\( 135 \, \text{m}^3 \)[/tex]



Answer :

To calculate the volume of a right circular cylinder, we can use the formula:

[tex]\[ \text{Volume} = \pi r^2 h \][/tex]

Where:
- [tex]\(\pi \approx 3\)[/tex] (as given in the problem for approximation purposes),
- [tex]\(r\)[/tex] is the radius of the cylinder,
- [tex]\(h\)[/tex] is the height of the cylinder.

Given:
- Radius [tex]\(r = 3\)[/tex] meters,
- Height [tex]\(h = 5\)[/tex] meters.

We substitute the given values into the formula:

[tex]\[ \text{Volume} = 3 \times (3)^2 \times 5 \][/tex]

First, calculate the square of the radius:

[tex]\[ (3)^2 = 3 \times 3 = 9 \][/tex]

Next, multiply this result by the constant [tex]\(\pi\)[/tex]:

[tex]\[ 3 \times 9 = 27 \][/tex]

Finally, multiply by the height:

[tex]\[ 27 \times 5 = 135 \][/tex]

Thus, the volume of the cylinder is:

[tex]\[ \text{Volume} = 135 \, \text{m}^3 \][/tex]

The correct answer from the given choices is:

D. [tex]\(135 \, \text{m}^3\)[/tex]