The volume of a container measures 4,000 mm3 and contains 50 marbles each marble has a radius of 2 mm used 3.14 as an approximation for pi how much space in the boxes unmeasured around your answer to the nearest tenth
To find the total volume occupied by the marbles, we can calculate the volume of one marble and multiply it by the total number of marbles.
The volume of a sphere (marble) is given by the formula:
V = (4/3) * π * r^3
where r is the radius.
Let's calculate the volume of one marble:
V_marble = (4/3) * 3.14 * 2^3
= (4/3) * 3.14 * 8
≈ 33.51 mm^3
Now, let's find the total volume occupied by the 50 marbles:
V_total = V_marble * 50
≈ 33.51 * 50
≈ 1675.5 mm^3
The remaining volume in the container can be found by subtracting the total volume occupied by the marbles from the total volume of the container:
Remaining volume = Container volume - V_total
= 4000 - 1675.5
≈ 2324.5 mm^3
Therefore, the space in the box unmeasured is approximately 2324.5 mm^3.