To find the volume [tex]\(V\)[/tex] of a cylinder, we use the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( \pi \)[/tex] (pi) is approximately 3.14159,
- [tex]\( r \)[/tex] is the radius of the base of the cylinder,
- [tex]\( h \)[/tex] is the height of the cylinder.
Given:
- [tex]\( r = 3 \)[/tex] centimeters,
- [tex]\( h = 10 \)[/tex] centimeters.
First, we calculate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = (3 \text{ cm})^2 = 9 \text{ cm}^2 \][/tex]
Next, we multiply [tex]\( r^2 \)[/tex] by [tex]\( h \)[/tex]:
[tex]\[ r^2 \times h = 9 \text{ cm}^2 \times 10 \text{ cm} = 90 \text{ cm}^3 \][/tex]
Now, we multiply this result by [tex]\( \pi \)[/tex]:
[tex]\[ V = \pi \times 90 \text{ cm}^3 \][/tex]
Thus, the volume [tex]\( V \)[/tex] of the cylinder is:
[tex]\[ V \approx 3.14159 \times 90 \text{ cm}^3 = 282.7433388230814 \text{ cm}^3 \][/tex]
So, the volume [tex]\( V \)[/tex] when [tex]\( r \)[/tex] is 3 centimeters and [tex]\( h \)[/tex] is 10 centimeters is approximately:
[tex]\[ 282.7433388230814 \text{ cm}^3 \][/tex]
