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.
The total volume of the marbles can be found by calculating the volume of one marble and multiplying it by the number of marbles.
The formula to calculate the volume of a sphere is given by V = (4/3) * π * r^3, where V is the volume and r is the radius.
Given that each marble has a radius of 2 mm, the volume of one marble is:
V_marble = (4/3) * 3.14 * 2^3
= (4/3) * 3.14 * 8
= 33.4933 mm^3 (rounded to the nearest tenth)
The total volume of the marbles is therefore:
V_total_marbles = 33.4933 mm^3/marble * 50 marbles
= 1674.665 mm^3 (rounded to the nearest tenth)
To find the unused space in the box, subtract the total volume of the marbles from the volume of the container:
Unused space = Volume of container - Volume of marbles
= 4000 mm^3 - 1674.665 mm^3
= 2325.335 mm^3 (rounded to the nearest tenth)
Therefore, the space unused in the box is approximately 2325.3 mm^3.