Question
Robert is pouring wax into cylindrical candle containers. Approximately 226.19 cubic inches of wax fill one candle jar. Which image represents that volume?
A cylinder with height 8 inches and radius 3 inches.
A cylinder with height 5 inches and radius 4 inches.
A cylinder with height 10 inches and radius 2 inches.
A cylinder with height 5 inches and radius 5 inches.
A cylinder with height 8 inches and radius 3 inches.
A cylinder with height 5 inches and radius 4 inches.
A cylinder with height 10 inches and radius 2 inches.
A cylinder with height 5 inches and radius 5 inches.
Answers
GPT-4o mini
To determine which cylinder holds approximately 226.19 cubic inches, we can use the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cylinder. We will calculate the volume for each option provided.
1. **Cylinder with height 8 inches and radius 3 inches:**
\[
V = \pi (3^2)(8) = \pi (9)(8) = 72\pi \approx 226.19 \text{ cubic inches} \quad (\text{since } \pi \approx 3.14)
\]
\[
V \approx 72 \times 3.14 \approx 226.08 \text{ cubic inches}
\]
2. **Cylinder with height 5 inches and radius 4 inches:**
\[
V = \pi (4^2)(5) = \pi (16)(5) = 80\pi \approx 251.2 \text{ cubic inches}
\]
3. **Cylinder with height 10 inches and radius 2 inches:**
\[
V = \pi (2^2)(10) = \pi (4)(10) = 40\pi \approx 125.6 \text{ cubic inches}
\]
4. **Cylinder with height 5 inches and radius 5 inches:**
\[
V = \pi (5^2)(5) = \pi (25)(5) = 125\pi \approx 392.5 \text{ cubic inches}
\]
From these calculations, the only cylinder that approximates the volume of 226.19 cubic inches is:
**A cylinder with height 8 inches and radius 3 inches.**
\[
V = \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cylinder. We will calculate the volume for each option provided.
1. **Cylinder with height 8 inches and radius 3 inches:**
\[
V = \pi (3^2)(8) = \pi (9)(8) = 72\pi \approx 226.19 \text{ cubic inches} \quad (\text{since } \pi \approx 3.14)
\]
\[
V \approx 72 \times 3.14 \approx 226.08 \text{ cubic inches}
\]
2. **Cylinder with height 5 inches and radius 4 inches:**
\[
V = \pi (4^2)(5) = \pi (16)(5) = 80\pi \approx 251.2 \text{ cubic inches}
\]
3. **Cylinder with height 10 inches and radius 2 inches:**
\[
V = \pi (2^2)(10) = \pi (4)(10) = 40\pi \approx 125.6 \text{ cubic inches}
\]
4. **Cylinder with height 5 inches and radius 5 inches:**
\[
V = \pi (5^2)(5) = \pi (25)(5) = 125\pi \approx 392.5 \text{ cubic inches}
\]
From these calculations, the only cylinder that approximates the volume of 226.19 cubic inches is:
**A cylinder with height 8 inches and radius 3 inches.**