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
1,674.7 mm3
1,674.7 mm cubed
2,325.3 mm3
2,325.3 mm cubed
33.5 mm3
33.5 mm cubed
3,900 mm3
The volume of each marble can be calculated using the formula for the volume of a sphere, which is V = (4/3)πr^3. Plugging in the radius of 2 mm, we get V = (4/3)(3.14)(2^3) = 33.493 mm^3 (rounded to three decimal places).
To find the total volume occupied by the marbles, we multiply the volume of each marble by the number of marbles: 33.493 mm^3/marble * 50 marbles = 1,674.65 mm^3 (rounded to two decimal places).
To find the space unused, we subtract the volume occupied by the marbles from the total volume of the container: 4,000 mm^3 - 1,674.65 mm^3 = 2,325.35 mm^3 (rounded to two decimal places).
Therefore, the answer is 2,325.3 mm^3 (rounded to one decimal place).