To find the volume of a cylinder, we use the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( \pi \)[/tex] is a mathematical constant (approximately 3.14159, but for this problem, we will use the given value [tex]\(\pi = \frac{22}{7}\)[/tex]),
- [tex]\( r \)[/tex] is the radius of the base of the cylinder,
- [tex]\( h \)[/tex] is the height of the cylinder.
Given:
- The radius [tex]\( r = 6 \)[/tex] cm,
- The height [tex]\( h = 14 \)[/tex] cm,
- [tex]\(\pi = \frac{22}{7}\)[/tex].
First, calculate the area of the base of the cylinder. The area [tex]\( A \)[/tex] of a circle is given by:
[tex]\[ A = \pi r^2 \][/tex]
Substitute the radius and the value of [tex]\(\pi\)[/tex]:
[tex]\[ A = \frac{22}{7} \times (6)^2 \][/tex]
[tex]\[ A = \frac{22}{7} \times 36 \][/tex]
[tex]\[ A = \frac{22 \times 36}{7} \][/tex]
[tex]\[ A = \frac{792}{7} \][/tex]
[tex]\[ A = 113.14 \text{ cm}^2 \][/tex]
Next, use this area to find the volume:
[tex]\[ V = A \times h \][/tex]
[tex]\[ V = 113.14 \text{ cm}^2 \times 14 \text{ cm} \][/tex]
[tex]\[ V = 1584.0 \text{ cm}^3 \][/tex]
Thus, the volume of the cylinder is [tex]\( 1584.0 \text{ cm}^3 \)[/tex].
The correct answer is:
E. [tex]\( 1584 \text{ cm}^3 \)[/tex]
