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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)
To find out how much space in the container is empty, you need to calculate the total volume of the tennis balls and subtract it from the volume of the container.
Let's start by calculating the volume of a single tennis ball 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.
Given that the radius of a tennis ball is 2.5 in, we can substitute this value into the formula:
V = (4/3) * 3.14 * (2.5 in)^3
V ≈ (4/3) * 3.14 * (15.625 in^3)
V ≈ 65.44 in^3
Now, we can calculate the total volume of all the tennis balls by multiplying the volume of a single tennis ball by the number of tennis balls:
Total volume of tennis balls = 65.44 in^3/ball * 12 balls
Total volume of tennis balls ≈ 785.28 in^3
Finally, subtract the total volume of the tennis balls from the volume of the container to determine the amount of space that is empty:
Empty space = Volume of container - Total volume of tennis balls
Empty space = 3200 in^3 - 785.28 in^3
Empty space ≈ 2414.72 in^3
Therefore, the amount of space in the container that is empty is approximately 2415 in^3.
Thanks That worked and now I know what to do
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The volume of a container measures 4,000 mm3 and contains 50 marbles. Each marble has a radius of 2 mm. Use 3.14 as an approximation for pi. How much space in the box is unused? Round your answer to the nearest tenth.(1 point)
To find out how much space in the box is unused, you need to calculate the total volume of the marbles and subtract it from the volume of the container.
Let's start by calculating the volume of a single marble 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.
Given that the radius of a marble is 2 mm, we can convert it to mm and substitute the value into the formula:
V = (4/3) * 3.14 * (2 mm)^3
V ≈ (4/3) * 3.14 * (8 mm^3)
V ≈ 33.493 mm^3
Now, we can calculate the total volume of all the marbles by multiplying the volume of a single marble by the number of marbles:
Total volume of marbles = 33.493 mm^3/marble * 50 marbles
Total volume of marbles ≈ 1674.65 mm^3
Finally, subtract the total volume of the marbles from the volume of the container to determine the amount of space that is unused:
Unused space = Volume of container - Total volume of marbles
Unused space = 4000 mm^3 - 1674.65 mm^3
Unused space ≈ 2325.35 mm^3
Therefore, the amount of space in the box that is unused is approximately 2325.35 mm^3.
Kairay created a sculpture by forming a hemisphere with a radius of 20 inches and then removing a hemisphere with a radius of 15 inches from it. Calculate the volume of his sculpture. Use 3.14 as an approximation for pi. Round your answer to the nearest whole number.(1 point)
Responses
7,065 in.3
7,065 inches cubed
16,747 in.3
16,747 inches cubed
9,682 in.3
9,682 inches cubed
19,363 in.3
19,363 inches cubed
To calculate the volume of Kairay's sculpture, we need to find the volume of the larger hemisphere and subtract the volume of the smaller hemisphere.
Let's start with the volume of a hemisphere using the formula: V = (2/3) * π * r^3.
For the larger hemisphere with a radius of 20 inches:
V1 = (2/3) * 3.14 * (20 inches)^3
V1 ≈ (2/3) * 3.14 * (8000 inches^3)
V1 ≈ 33546.67 inches^3
For the smaller hemisphere with a radius of 15 inches:
V2 = (2/3) * 3.14 * (15 inches)^3
V2 ≈ (2/3) * 3.14 * (3375 inches^3)
V2 ≈ 14137.5 inches^3
Now, we can calculate the volume of Kairay's sculpture by subtracting V2 from V1:
Volume of sculpture = V1 - V2
Volume of sculpture ≈ 33546.67 inches^3 - 14137.5 inches^3
Volume of sculpture ≈ 19409.17 inches^3
Therefore, the volume of Kairay's sculpture is approximately 19,409 in.3 (rounded to the nearest whole number).