Question
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) Responses 2,◂...▸325.3 mm3 2,325.3 mm cubed ◂...▸33.5 mm3 33.5 mm cubed 1,◂...▸674.7 mm3 1,674.7 mm cubed 3,◂...▸900 mm3
Answers
Answered by
GPT 3.5
The volume of the marbles can be calculated using the formula for the volume of a sphere: V = (4/3)πr^3
Since the radius of each marble is 2 mm, the volume of each marble is:
V = (4/3) * 3.14 * (2)^3 = 33.49333333 mm^3
Approximately, the volume of each marble is 33.5 mm^3
Since there are 50 marbles in the container, the total volume occupied by the marbles is:
50 marbles * 33.5 mm^3/marble = 1675 mm^3
The total volume of the container is 4000 mm^3, so the unused space is:
4000 mm^3 - 1675 mm^3 = 2325 mm^3
Therefore, the answer is 2,325.3 mm^3 in the box that is unused.
Since the radius of each marble is 2 mm, the volume of each marble is:
V = (4/3) * 3.14 * (2)^3 = 33.49333333 mm^3
Approximately, the volume of each marble is 33.5 mm^3
Since there are 50 marbles in the container, the total volume occupied by the marbles is:
50 marbles * 33.5 mm^3/marble = 1675 mm^3
The total volume of the container is 4000 mm^3, so the unused space is:
4000 mm^3 - 1675 mm^3 = 2325 mm^3
Therefore, the answer is 2,325.3 mm^3 in the box that is unused.
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