To find the volume of a cylinder, we can use the formula for the volume [tex]\( V \)[/tex] of a cylinder:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( \pi \)[/tex] (Pi) is a constant approximately equal to 3.14159,
- [tex]\( r \)[/tex] is the radius of the base of the cylinder, and
- [tex]\( h \)[/tex] is the height of the cylinder.
Given the following dimensions:
- Height [tex]\( h = 16.9 \)[/tex] inches,
- Diameter of the base [tex]\( d = 9.6 \)[/tex] inches.
### Step-by-Step Solution:
1. Calculate the radius [tex]\( r \)[/tex]:
The radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[
r = \frac{d}{2} = \frac{9.6}{2} = 4.8 \, \text{inches}
\][/tex]
2. Apply the volume formula for the cylinder:
[tex]\[
V = \pi r^2 h
\][/tex]
Plugging in the values we have:
[tex]\[
V = \pi (4.8)^2 (16.9)
\][/tex]
3. Square the radius [tex]\( r \)[/tex]:
[tex]\[
4.8^2 = 23.04
\][/tex]
4. Multiply by height [tex]\( h \)[/tex]:
[tex]\[
23.04 \times 16.9 = 389.376
\][/tex]
5. Multiply by [tex]\( \pi \)[/tex]:
[tex]\[
V = \pi \times 389.376 \approx 1223.2607810841791 \, \text{cubic inches}
\][/tex]
6. Round to the nearest tenth:
The nearest tenth of [tex]\( 1223.2607810841791 \)[/tex] is [tex]\( 1223.3 \)[/tex].
### Final Answer:
The volume of the cylinder, rounded to the nearest tenth of a cubic inch, is [tex]\( 1223.3 \, \text{cubic inches} \)[/tex].
