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)
in.3
The volume of each tennis ball can be calculated using the formula for the volume of a sphere: V = 4/3 * π * r^3.
Substituting the given values:
V = 4/3 * 3.14 * (2.5)^3 = 4/3 * 3.14 * 15.625 ≈ 65.45 in.3
The total volume of all the tennis balls can be calculated by multiplying the volume of one tennis ball (65.45 in.3) by the number of tennis balls (12):
Total volume of tennis balls = 65.45 * 12 ≈ 785.4 in.3
To find the empty space in the container, subtract the total volume of the tennis balls from the volume of the container:
Empty space = 3200 - 785.4 ≈ 2414.6 in.3
Therefore, the space in the container that is empty is approximately 2,414.6 in.3.
incorrect
I apologize for the incorrect response. Let me recalculate:
The volume of each tennis ball can be calculated using the formula for the volume of a sphere: V = 4/3 * π * r^3.
Substituting the given value:
V = 4/3 * 3.14 * (2.5)^3 ≈ 65.45 in.3
The total volume of all the tennis balls can be calculated by multiplying the volume of one tennis ball (65.45 in.3) by the number of tennis balls (12):
Total volume of tennis balls = 65.45 * 12 = 785.4 in.3
To find the empty space in the container, subtract the total volume of the tennis balls from the volume of the container:
Empty space = 3200 - 785.4 = 2414.6 in.3
Therefore, the space in the container that is empty is approximately 2,414.6 in.3.
wrong agian do it another way
I apologize for the confusion. Let's try another approach to find the empty space in the container.
The volume of the container is given as 3,200 in^3. The volume of each tennis ball can be calculated using the formula for the volume of a sphere: V = 4/3 * π * r^3.
Substituting the given radius value of 2.5 in:
V = 4/3 * 3.14 * (2.5)^3
Simplifying the calculation:
V = 4/3 * 3.14 * 15.625 ≈ 65.45 in^3 (rounded to two decimal places)
Now, let's find the total volume occupied by the tennis balls in the container. Since there are a dozen tennis balls, the total volume is:
Total volume of tennis balls = 65.45 * 12 ≈ 785.4 in^3
To find the empty space in the container, subtract the total volume of the tennis balls from the volume of the container:
Empty space = 3,200 - 785.4 ≈ 2,414.6 in^3
Therefore, the space in the container that is empty is approximately 2,414.6 in^3.