The volume of a container measures 4,000mm³ and contains 50 marbles each marble has a radius of 2mm use 3.14 as an approximation for pi how much space in the box is unused round your answer to the nearest tenth
The volume of one marble can be calculated using the formula for the volume of a sphere:
V = (4/3) * π * r³
where V is the volume and r is the radius of the marble. Substituting the given values:
V = (4/3) * 3.14 * 2³ = (4/3) * 3.14 * 8 = 33.4933 mm³ (approx)
The total volume occupied by 50 marbles can be calculated by multiplying the volume of one marble by the number of marbles:
Total volume occupied = 33.4933 mm³ * 50 = 1674.665 mm³ (approx)
The unused space in the box can be calculated by subtracting the total volume occupied by the marbles from the volume of the container:
Unused space = 4000 mm³ - 1674.665 mm³ = 2325.335 mm³ (approx)
Rounded to the nearest tenth, the unused space in the box is approximately 2325.3 mm³.