The volume of a container measures 4,000 mm^3 and contains 50 marbles each marble has a radius of two mm used 3.14 as an approximation for pie how much space in the box is used around your answer to the nearest tenth

Answer 1

To find the space used by the marbles in the box, we first need to calculate the volume occupied by one marble.

The volume of a sphere is given by the formula V = (4/3) * π * r³, where r is the radius of the sphere.

Using the radius given (2 mm), we can calculate the volume of one marble:
V_marble = (4/3) * 3.14 * 2^3
V_marble ≈ 33.49 mm³

Since there are 50 marbles in the box, the total volume occupied by the marbles is given by:
Total volume = V_marble * 50
Total volume ≈ 1674.5 mm³

Now, to find the space used by the marbles in the box, we subtract the total volume occupied by the marbles from the volume of the container:
Space used = Volume of container - Total volume occupied by marbles
Space used = 4000 mm³ - 1674.5 mm³
Space used ≈ 2325.5 mm³

Therefore, the space used by the marbles in the box is approximately 2325.5 mm³ when rounded to the nearest tenth.