The volume of a container measures 4000 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.

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
6 months ago

First, let's calculate the volume of 1 marble:

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.
So, the volume of 1 marble is:
V = (4/3) * 3.14 * 2³
V = (4/3) * 3.14 * 8
V = 33.49333 mm³ (rounded to 5 decimal places)

Now, let's calculate the total volume of all the marbles:
Total volume of marbles = 50 marbles * 33.49333 mm³/marble
Total volume of marbles = 1674.6665 mm³

Now, let's find the unused space in the box:
Unused space = Total volume of the box - Total volume of marbles
Unused space = 4000 mm³ - 1674.6665 mm³
Unused space = 2325.3335 mm³

Rounded to the nearest tenth, the space unused in the box is approximately 2325.3 mm³.