Question
Al has a cylindrical storage container 30 centimeters tall with a diameter of 22 centimeters. How much bird food in cubic centimeters will fit in the container? Use the formula V = Bh and approximate π
using 3.14. Round your answer to the nearest tenth.
using 3.14. Round your answer to the nearest tenth.
Answers
GPT-4o mini
To find the volume of the cylindrical storage container, we will use the formula for the volume of a cylinder, which is given by:
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height of the cylinder.
1. **Find the radius**: The diameter of the cylinder is 22 cm, so the radius \( r \) is half of the diameter.
\[
r = \frac{22 \, \text{cm}}{2} = 11 \, \text{cm}
\]
2. **Height of the cylinder**: The height \( h \) is given as 30 cm.
3. **Calculate the volume**: Now, we can substitute the values into the volume formula. Using \( \pi \approx 3.14 \):
\[
V = 3.14 \times (11 \, \text{cm})^2 \times 30 \, \text{cm}
\]
Calculating \( (11 \, \text{cm})^2 \):
\[
(11 \, \text{cm})^2 = 121 \, \text{cm}^2
\]
Now substitute:
\[
V = 3.14 \times 121 \, \text{cm}^2 \times 30 \, \text{cm}
\]
Calculating the multiplication:
\[
121 \, \text{cm}^2 \times 30 \, \text{cm} = 3630 \, \text{cm}^3
\]
Now calculate the final volume:
\[
V = 3.14 \times 3630 \, \text{cm}^3
\]
Calculating this gives:
\[
V = 11340.2 \, \text{cm}^3
\]
4. **Round to the nearest tenth**:
The volume of bird food that will fit in the container is
\[
\boxed{11340.2 \, \text{cm}^3}
\]
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height of the cylinder.
1. **Find the radius**: The diameter of the cylinder is 22 cm, so the radius \( r \) is half of the diameter.
\[
r = \frac{22 \, \text{cm}}{2} = 11 \, \text{cm}
\]
2. **Height of the cylinder**: The height \( h \) is given as 30 cm.
3. **Calculate the volume**: Now, we can substitute the values into the volume formula. Using \( \pi \approx 3.14 \):
\[
V = 3.14 \times (11 \, \text{cm})^2 \times 30 \, \text{cm}
\]
Calculating \( (11 \, \text{cm})^2 \):
\[
(11 \, \text{cm})^2 = 121 \, \text{cm}^2
\]
Now substitute:
\[
V = 3.14 \times 121 \, \text{cm}^2 \times 30 \, \text{cm}
\]
Calculating the multiplication:
\[
121 \, \text{cm}^2 \times 30 \, \text{cm} = 3630 \, \text{cm}^3
\]
Now calculate the final volume:
\[
V = 3.14 \times 3630 \, \text{cm}^3
\]
Calculating this gives:
\[
V = 11340.2 \, \text{cm}^3
\]
4. **Round to the nearest tenth**:
The volume of bird food that will fit in the container is
\[
\boxed{11340.2 \, \text{cm}^3}
\]