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Answer :
To determine the volume of sand in the container and convert it to gallons, we can follow these steps:
1. Understand the Shape and Measurements:
- The container is a cylinder.
- The height of the cylinder is 10 inches.
- The diameter of the cylinder is 12 inches.
2. Calculate the Radius:
- The radius [tex]\( r \)[/tex] is half of the diameter, so:
[tex]\[
r = \frac{12}{2} = 6 \text{ inches}
\][/tex]
3. Calculate the Volume of the Cylinder:
- The formula for the volume [tex]\( V \)[/tex] of a cylinder is:
[tex]\[
V = \pi r^2 h
\][/tex]
- Plug the values into the formula:
[tex]\[
V = \pi \times (6^2) \times 10
\][/tex]
- Calculate [tex]\( 6^2 \)[/tex]:
[tex]\[
6^2 = 36
\][/tex]
- So, the volume [tex]\( V \)[/tex] is:
[tex]\[
V = \pi \times 36 \times 10 = 360\pi \, \text{cubic inches}
\][/tex]
4. Convert Cubic Inches to Gallons:
- Given that there are 231 cubic inches in one gallon:
- The number of gallons of sand is:
[tex]\[
\frac{360\pi}{231}
\][/tex]
5. Calculate the Approximate Volume in Gallons:
- Use the value of [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[
360 \times 3.14159 \approx 1130.9736
\][/tex]
- Then, divide 1130.9736 by 231:
[tex]\[
\frac{1130.9736}{231} \approx 4.894
\][/tex]
6. Round to the Nearest Gallon:
- Rounding 4.894 to the nearest whole number gives us approximately 5 gallons.
Therefore, the approximate volume of sand in the container is 5 gallons.
1. Understand the Shape and Measurements:
- The container is a cylinder.
- The height of the cylinder is 10 inches.
- The diameter of the cylinder is 12 inches.
2. Calculate the Radius:
- The radius [tex]\( r \)[/tex] is half of the diameter, so:
[tex]\[
r = \frac{12}{2} = 6 \text{ inches}
\][/tex]
3. Calculate the Volume of the Cylinder:
- The formula for the volume [tex]\( V \)[/tex] of a cylinder is:
[tex]\[
V = \pi r^2 h
\][/tex]
- Plug the values into the formula:
[tex]\[
V = \pi \times (6^2) \times 10
\][/tex]
- Calculate [tex]\( 6^2 \)[/tex]:
[tex]\[
6^2 = 36
\][/tex]
- So, the volume [tex]\( V \)[/tex] is:
[tex]\[
V = \pi \times 36 \times 10 = 360\pi \, \text{cubic inches}
\][/tex]
4. Convert Cubic Inches to Gallons:
- Given that there are 231 cubic inches in one gallon:
- The number of gallons of sand is:
[tex]\[
\frac{360\pi}{231}
\][/tex]
5. Calculate the Approximate Volume in Gallons:
- Use the value of [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[
360 \times 3.14159 \approx 1130.9736
\][/tex]
- Then, divide 1130.9736 by 231:
[tex]\[
\frac{1130.9736}{231} \approx 4.894
\][/tex]
6. Round to the Nearest Gallon:
- Rounding 4.894 to the nearest whole number gives us approximately 5 gallons.
Therefore, the approximate volume of sand in the container is 5 gallons.
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