Let's break down the questions and find the required calculations step by step.
Part 1: Volume of the container
Step 1: Determine the radius of the container.
We don't have the value yet, so let's assume the radius \( r \) is given. For simplicity, let’s say the radius is 3 inches (you can replace this with the actual value if provided).
\[ r = 3 , \text{inches} \]
Step 2: Determine the area of the circular base of the container.
The area \( A \) of the circular base can be calculated using the formula for the area of a circle: \[ A = \pi r^2 \] Using \( \pi \approx 3.14 \): \[ A = 3.14 \times (3)^2 = 3.14 \times 9 = 28.26 , \text{square inches} \]
Step 3: Determine the volume of the container.
Assuming the height \( h \) of the container is given, let’s say \( h = 10 \) inches. The volume \( V \) can be calculated using the formula for the volume of a cylinder: \[ V = A \times h = 28.26 \times 10 = 282.6 , \text{cubic inches} \]
Part 2: Volume of the Rectangular Prism
Step 1: Determine the area of the base of the rectangular prism.
The base area \( A \) is calculated by multiplying the dimensions: \[ \text{Area} = \text{width} \times \text{length} = 22 , \text{inches} \times 7.6 , \text{inches} = 167.2 , \text{square inches} \]
Step 2: Determine the volume of the rectangular prism.
The volume \( V \) is calculated as follows: \[ V = A \times h = 167.2 \times 15 = 2508 , \text{cubic inches} \]
Part 3: Will the 6 popcorn containers fit?
Step 1: Determine the total volume of the 6 popcorn containers.
Assuming the volume of each container is 282.6 cubic inches, the combined volume for the 6 containers is: \[ \text{Total volume} = 6 \times 282.6 = 1695.6 , \text{cubic inches} \]
Step 2: Check if the containers fit in the rectangular prism and find leftover space.
Now, we will determine if the total volume of the popcorn containers fits in the rectangular prism: \[ \text{Space left} = \text{Volume of rectangular prism} - \text{Total volume of containers} \] \[ \text{Space left} = 2508 - 1695.6 = 812.4 , \text{cubic inches} \]
Final Responses
- Radius of the container: 3 inches (replace with actual value if provided).
- Area of the circular base of the container: 28.26 square inches.
- Volume of the container: 282.6 cubic inches.
- Area of the base of the rectangular prism: 167.2 square inches.
- Volume of the rectangular prism: 2508 cubic inches.
- Will the containers fit? Yes, there will be about 812.4 cubic inches of space left.
Given the options in the last question, if adjusted with actual parameters provided, the answer should align with the calculated leftover space. Adjust the numbers based on actual measurements as needed.