Question
At the beach, you use your pail to dig a circular pool in the sand 3 feet in diameter and 18 inches deep. The pail is 1312
inches tall and 8 inches in diameter. How many full pails of sand did you dig to carve out the pool?(1 point)
inches tall and 8 inches in diameter. How many full pails of sand did you dig to carve out the pool?(1 point)
Answers
GPT-4o mini
To determine how many full pails of sand you dug to carve out the pool, we will first calculate the volume of the circular pool in the sand and then the volume of the pail.
1. **Volume of the Pool**:
The pool is circular with a diameter of 3 feet (or 36 inches) and a depth of 18 inches. We can calculate the volume \( V \) of the pool using the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height (depth).
- Convert the diameter to radius:
\[
r = \frac{3 \text{ ft}}{2} = \frac{36 \text{ inches}}{2} = 18 \text{ inches}
\]
- Depth \( h = 18 \text{ inches} \).
Now, calculate the volume of the pool:
\[
V = \pi (18)^2 (18)
\]
\[
V = \pi (324) (18) = \pi (5832) \text{ cubic inches}
\]
\[
V \approx 18334.95 \text{ cubic inches} \quad (\text{using } \pi \approx 3.14159)
\]
2. **Volume of the Pail**:
The pail has a diameter of 8 inches (which gives a radius of 4 inches) and a height of 1312 inches. The volume of the pail can again be calculated using the cylinder volume formula:
\[
V = \pi r^2 h
\]
where \( r = 4 \text{ inches} \) and \( h = 1312 \text{ inches} \).
Now, calculate the volume of the pail:
\[
V = \pi (4)^2 (1312)
\]
\[
V = \pi (16) (1312) = \pi (20992) \text{ cubic inches}
\]
\[
V \approx 65970.83 \text{ cubic inches} \quad (\text{using } \pi \approx 3.14159)
\]
3. **Calculating the Number of Full Pails**:
Now we divide the volume of the pool by the volume of the pail to find out how many full pails are needed:
\[
\text{Number of pails} = \frac{\text{Volume of the pool}}{\text{Volume of the pail}} = \frac{5832\pi}{20992\pi} = \frac{5832}{20992} \approx 0.277
\]
Since we need the number of **full** pails, we round down (since you cannot have a fraction of a pail):
\[
\text{Number of full pails} = 0
\]
Thus, you dug out approximately 0 full pails of sand to carve out the pool. If you were thinking about an interpretation mistake or looking for calculation changes, please clarify.
1. **Volume of the Pool**:
The pool is circular with a diameter of 3 feet (or 36 inches) and a depth of 18 inches. We can calculate the volume \( V \) of the pool using the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height (depth).
- Convert the diameter to radius:
\[
r = \frac{3 \text{ ft}}{2} = \frac{36 \text{ inches}}{2} = 18 \text{ inches}
\]
- Depth \( h = 18 \text{ inches} \).
Now, calculate the volume of the pool:
\[
V = \pi (18)^2 (18)
\]
\[
V = \pi (324) (18) = \pi (5832) \text{ cubic inches}
\]
\[
V \approx 18334.95 \text{ cubic inches} \quad (\text{using } \pi \approx 3.14159)
\]
2. **Volume of the Pail**:
The pail has a diameter of 8 inches (which gives a radius of 4 inches) and a height of 1312 inches. The volume of the pail can again be calculated using the cylinder volume formula:
\[
V = \pi r^2 h
\]
where \( r = 4 \text{ inches} \) and \( h = 1312 \text{ inches} \).
Now, calculate the volume of the pail:
\[
V = \pi (4)^2 (1312)
\]
\[
V = \pi (16) (1312) = \pi (20992) \text{ cubic inches}
\]
\[
V \approx 65970.83 \text{ cubic inches} \quad (\text{using } \pi \approx 3.14159)
\]
3. **Calculating the Number of Full Pails**:
Now we divide the volume of the pool by the volume of the pail to find out how many full pails are needed:
\[
\text{Number of pails} = \frac{\text{Volume of the pool}}{\text{Volume of the pail}} = \frac{5832\pi}{20992\pi} = \frac{5832}{20992} \approx 0.277
\]
Since we need the number of **full** pails, we round down (since you cannot have a fraction of a pail):
\[
\text{Number of full pails} = 0
\]
Thus, you dug out approximately 0 full pails of sand to carve out the pool. If you were thinking about an interpretation mistake or looking for calculation changes, please clarify.