To determine the volume of Alexis's cylindrical trash can, we need to use the formula for the volume of a cylinder, which is given by:
[tex]\[ V = \pi r^2 h \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( r \)[/tex] is the radius of the base of the cylinder, and [tex]\( h \)[/tex] is the height of the cylinder.
1. Find the radius of the cylindrical trash can:
- We are given the diameter of the trash can, which is 24 cm.
- The radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[ r = \frac{\text{diameter}}{2} = \frac{24 \, \text{cm}}{2} = 12 \, \text{cm} \][/tex]
2. Plug the radius and height into the volume formula:
- The height [tex]\( h \)[/tex] of the cylinder is given as 42 cm.
[tex]\[ V = \pi \times (12 \, \text{cm})^2 \times 42 \, \text{cm} \][/tex]
3. Calculate the volume:
- Compute the squared radius:
[tex]\[ 12 \, \text{cm} \times 12 \, \text{cm} = 144 \, \text{cm}^2 \][/tex]
- Multiply by the height and then by π:
[tex]\[ V = \pi \times 144 \, \text{cm}^2 \times 42 \, \text{cm} \][/tex]
4. Approximate the volume:
- The multiplication of these values results in:
[tex]\[ V \approx 19000.35236891107 \, \text{cm}^3 \][/tex]
Therefore, the approximate volume of Alexis's cylindrical trash can is most closely represented by option:
[tex]\[ \text{C } \, 19,000 \, \text{cm}^3 \][/tex]
