To determine the volume of the aluminum can, which is in the shape of a cylinder, we need to follow several steps:
1. Convert the mixed numbers to improper fractions:
- Diameter [tex]\( = 4 \frac{3}{4} \)[/tex] inches.
Convert [tex]\( 4 \frac{3}{4} \)[/tex] to an improper fraction:
[tex]\[
4 \frac{3}{4} = 4 + \frac{3}{4} = \frac{16}{4} + \frac{3}{4} = \frac{19}{4}
\][/tex]
So, the diameter is [tex]\( 4.75 \)[/tex] inches when converted to a decimal.
- Height [tex]\( = 3 \frac{1}{5} \)[/tex] inches.
Convert [tex]\( 3 \frac{1}{5} \)[/tex] to an improper fraction:
[tex]\[
3 \frac{1}{5} = 3 + \frac{1}{5} = \frac{15}{5} + \frac{1}{5} = \frac{16}{5}
\][/tex]
So, the height is [tex]\( 3.2 \)[/tex] inches when converted to a decimal.
2. Calculate the radius of the cylinder:
- The diameter is [tex]\( 4.75 \)[/tex] inches.
- The radius is half of the diameter:
[tex]\[
\text{Radius} = \frac{4.75}{2} = 2.375 \text{ inches}
\][/tex]
3. Use the formula for the volume of a cylinder:
- The volume [tex]\( V \)[/tex] of a cylinder is given by:
[tex]\[
V = \pi r^2 h
\][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height.
4. Plug in the values for radius and height:
- Radius [tex]\( r = 2.375 \)[/tex] inches.
- Height [tex]\( h = 3.2 \)[/tex] inches.
- Calculate the volume [tex]\( V \)[/tex]:
[tex]\[
V = \pi (2.375)^2 (3.2)
\][/tex]
- First, calculate [tex]\( (2.375)^2 \)[/tex]:
[tex]\[
(2.375)^2 \approx 5.640625
\][/tex]
- Next, calculate [tex]\( 5.640625 \times 3.2 \)[/tex]:
[tex]\[
5.640625 \times 3.2 \approx 18.049
\][/tex]
- Finally, multiply by [tex]\( \pi \approx 3.14159 \)[/tex]:
[tex]\[
V \approx 3.14159 \times 18.049 \approx 56.7057
\][/tex]
So, the volume of the aluminum can is approximately [tex]\( 56.7057 \)[/tex] cubic inches.
