The volume of a container measures 3,200 in and contains a dozen of tennis balls. Each tennis ball has a radius of 2.5 in. How much space in the container is empty? Use 3.14 an an approximation for pi. Round to the nearest whole number, if necessary
The volume of a tennis ball can be calculated using the formula for the volume of a sphere: V = 4/3 * pi * r^3.
Plug in the given radius of 2.5 inches into the formula:
V = 4/3 * 3.14 * 2.5^3
V = 4/3 * 3.14 * 15.625
V = 65.45 cubic inches (approximately)
Since there are 12 tennis balls in the container, the total volume occupied by the tennis balls is:
12 * 65.45 = 785.4 cubic inches (approximately)
Therefore, the space empty in the container is:
3,200 - 785.4 = 2,414.6 cubic inches (approximately).
Rounded to the nearest whole number:
2,415 cubic inches.
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The volume of a container measures 4000 mm and contains 50 marbles. Each marble has a radius of 2 mm. Use 3.14 an an approximation for pi. How much space in the box is unused? Round your answer to the nearest tenth.
The volume of a marble can be calculated using the formula for the volume of a sphere: V = 4/3 * pi * r^3.
Plug in the given radius of 2 mm into the formula:
V = 4/3 * 3.14 * 2^3
V = 4/3 * 3.14 * 8
V = 33.493 cubic mm (approximated to the nearest thousandth).
Since there are 50 marbles in the container, the total volume occupied by the marbles is:
50 * 33.493 = 1674.65 cubic mm (approximated to the nearest hundredth).
Therefore, the unused space in the container is:
4000 - 1674.65 = 2325.35 cubic mm (approximated to the nearest hundredth).
Rounded to the nearest tenth:
2325.4 cubic mm.
To find the unused space in the box, we need to subtract the total volume occupied by the marbles from the volume of the box.
The volume of a marble can be calculated using the formula for the volume of a sphere: V = 4/3 * pi * r^3.
Let's calculate the volume of a marble:
V = 4/3 * 3.14 * 2^3
V = 4/3 * 3.14 * 8
V = 33.493 cubic mm (rounding to three decimal places).
Now, let's calculate the total volume occupied by the marbles:
Total Volume = 50 * 33.493 = 1674.65 cubic mm (rounding to two decimal places).
To find the unused space in the box, we subtract the total volume occupied by the marbles from the volume of the box:
Unused Space = 4000 - 1674.65 = 2325.35 cubic mm (rounding to two decimal places).
Rounded to the nearest tenth, the unused space in the box is 2325.4 cubic mm.
None of the given options are correct.
if you had to choose one,
If we had to choose one of the given options, the closest answer would be B. 2325.3.
Kairay created a sculpture by forming a hemisphere with a radius of 20 and then removing a hemisphere with a radius of 15 from it, Calculate the volume of his sculpture. Use 3.14 as an approximation for pi. Round your answer to the nearest whole number.
The volume of a hemisphere can be calculated using the formula: V = 2/3 * pi * r^3.
First, let's calculate the volume of the larger hemisphere:
V_large = 2/3 * 3.14 * 20^3
V_large = 2/3 * 3.14 * 8000
V_large = 33546.67 cubic units (rounded to two decimal places).
Next, let's calculate the volume of the smaller hemisphere:
V_small = 2/3 * 3.14 * 15^3
V_small = 2/3 * 3.14 * 3375
V_small = 7066.33 cubic units (rounded to two decimal places).
Finally, let's find the volume of the sculpture by subtracting the volume of the smaller hemisphere from the volume of the larger hemisphere:
Volume of sculpture = V_large - V_small
Volume of sculpture = 33546.67 - 7066.33
Volume of sculpture = 26480.34 cubic units (rounded to two decimal places).
Rounded to the nearest whole number, the volume of Kairay's sculpture is approximately 26,480 cubic units.