Question

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.(1 point) Responses 1,674.7 mm3 1,674.7 mm cubed 2,325.3 mm3 2,325.3 mm cubed 3,900 mm3 3,900 mm cubed 33.5 mm3

Answer 1

To find the total volume taken up by the marbles, we can calculate the volume of a single marble and then multiply it by the total number of marbles.

Volume of one marble = 4/3 * π * r^3
Volume of one marble = 4/3 * 3.14 * 2^3
Volume of one marble = 4/3 * 3.14 * 8
Volume of one marble = 33.4933 mm^3

Total volume taken up by the marbles = 33.4933 mm^3 * 50 = 1674.665 mm^3

Unused space in the box = Total volume of the box - Total volume taken up by the marbles
Unused space in the box = 4000 mm^3 - 1674.665 mm^3
Unused space in the box = 2325.335 mm^3

Rounded to the nearest tenth, the unused space in the box is 2325.3 mm^3. Therefore, the correct answer is:
2,325.3 mm cubed.