Sure! To find the volume of a cylinder, you can use the formula:
[tex]\[ \text{Volume} = \pi r^2 h \][/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.
From the question:
- The height [tex]\( h \)[/tex] is 16 inches.
- The diameter of the base is 4 inches.
First, find the radius of the base. The radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[ r = \frac{\text{diameter}}{2} = \frac{4 \, \text{inches}}{2} = 2 \, \text{inches} \][/tex]
Now, plug the values into the volume formula:
[tex]\[ \text{Volume} = \pi \times r^2 \times h \][/tex]
[tex]\[ \text{Volume} = \pi \times (2 \, \text{inches})^2 \times 16 \, \text{inches} \][/tex]
[tex]\[ \text{Volume} = \pi \times 4 \, \text{square inches} \times 16 \, \text{inches} \][/tex]
[tex]\[ \text{Volume} = \pi \times 64 \, \text{cubic inches} \][/tex]
[tex]\[ \text{Volume} \approx 3.14159 \times 64 \, \text{cubic inches} \][/tex]
[tex]\[ \text{Volume} \approx 201.06176 \, \text{cubic inches} \][/tex]
Finally, round the volume to the nearest tenths place:
[tex]\[ \text{Volume} \approx 201.1 \, \text{cubic inches} \][/tex]
So, the volume of the cylinder is approximately 201.1 cubic inches.
