The volume of a container measures 3,200 in.3 and contains a dozen tennis balls. Each tennis ball has a radius of 2.5 in. How much space in the container is empty? Use 3.14 as an approximation for pi. Round to the nearest whole number, if necessary.(1 point)
The volume of one tennis ball can be calculated using the formula for the volume of a sphere:
V = (4/3)*π*r^3
where V is the volume and r is the radius of the sphere.
Using a radius of 2.5 in and the approximation π ≈ 3.14, the volume of one tennis ball is:
V = (4/3)*3.14*(2.5^3)
V ≈ (4/3)*3.14*15.625
V ≈ 65.45
Since there are a dozen (12) tennis balls in the container, the total volume of the tennis balls is:
12 * 65.45 ≈ 785.4
To calculate the empty space in the container, we subtract the volume of the tennis balls from the total volume of the container:
3200 - 785.4 ≈ 2414.6
Therefore, there is approximately 2415 cubic inches of empty space in the container.
ty bot!
To find the amount of space that is empty in the container, we first need to calculate the volume occupied by the tennis balls and then subtract that from the total volume of the container.
The volume of a sphere can be calculated using the formula:
V = (4/3) * π * r^3
Given that the radius of each tennis ball is 2.5 inches, we can calculate the volume of one tennis ball:
V_ball = (4/3) * 3.14 * (2.5)^3
Next, we need to determine how many tennis balls can fit in the container. Since there are a dozen tennis balls, we know that there are 12 in total.
Now, we can calculate the volume occupied by the tennis balls:
V_total = V_ball * number of tennis balls
Finally, to find the empty space in the container, we subtract the volume occupied by the tennis balls from the total volume of the container:
Empty space = Total volume - V_total = 3,200 in^3 - V_total
Let's calculate the answer step by step:
1. Calculate the volume of one tennis ball:
V_ball = (4/3) * 3.14 * (2.5)^3 ≈ 65.45 in^3
2. Determine the number of tennis balls:
Number of tennis balls = 12
3. Calculate the volume occupied by the tennis balls:
V_total = V_ball * Number of tennis balls = 65.45 * 12 ≈ 785.4 in^3
4. Calculate the empty space in the container:
Empty space = Total volume - V_total
Empty space = 3,200 - 785.4 ≈ 2,414.6 in^3
Rounding to the nearest whole number:
Empty space ≈ 2,415 in^3
Therefore, the empty space in the container is approximately 2,415 cubic inches.