The total volume of the marbles can be calculated by finding the volume of a single marble first. The volume of a sphere is given by the formula V = (4/3) * pi * r^3. Plugging in the radius of 2 mm, we get V = (4/3) * 3.14 * 2^3 = 33.49 mm^3 (approximately 33.5 mm^3 when rounded to the nearest tenth).
Multiplying the volume of a single marble by the number of marbles (50) gives us the total volume of the marbles: 33.5 mm^3 * 50 = 1675 mm^3.
Subtracting the total volume of the marbles (1675 mm^3) from the total volume of the container (4000 mm^3) gives us the volume of the space unused in the box: 4000 mm^3 - 1675 mm^3 = 2325 mm^3.
Therefore, the correct answer is 2,325.3 mm^3 unused space.
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) Explain
Responses
2,325.3 mm3
2,325.3 mm cubed
1,674.7 mm3
1,674.7 mm cubed
33.5 mm3
33.5 mm cubed
3,900 mm3
1 answer
1 answer