To find the total volume occupied by the marbles, we can use the formula for the volume of a sphere: V = (4/3)Ď€r^3.
The radius of each marble is given as 2 mm, so we can substitute this value into the equation to find the volume of one marble: V = (4/3) * 3.14 * (2^3) = 33.49 mm^3 (rounded to two decimal places)
To find the total volume occupied by all 50 marbles, we can multiply the volume of one marble by the number of marbles: 33.49 mm^3 * 50 = 1674.5 mm^3.
To find the unused space in the container, we can subtract the total volume occupied by the marbles from the volume of the container: 4000 mm^3 - 1674.5 mm^3 = 2325.5 mm^3.
Rounding to the nearest tenth, the amount of space unused in the box is 2325.5 mm^3, which is closest to option 2,325.3 mm^3.
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
3,900 mm3
3,900 mm cubed
2,325.3 mm3
2,325.3 mm cubed
33.5 mm3
33.5 mm cubed
1,674.7 mm3
1 answer