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
3,900 mm3
3,900 mm cubed
33.5 mm3
33.5 mm cubed
1,674.7 mm3
1,674.7 mm cubed
2,325.3 mm3
To find the total volume of the marbles, we need to calculate the volume of one marble and then multiply it by the number of marbles. The volume of a sphere (marble) can be calculated using the formula V = (4/3)πr³, where V is the volume and r is the radius.
Using a radius of 2 mm and approximating pi as 3.14, the volume of one marble is:
V = (4/3) * 3.14 * (2)^3
V = 33.49333 mm³ (rounded to four decimal places)
Multiplying this volume by the number of marbles:
Total volume of marbles = 33.49333 mm³/marble * 50 marbles
Total volume of marbles = 1674.6665 mm³ (rounded to four decimal places)
To find the unused space in the box, subtract the volume of the marbles from the volume of the container:
Unused space = 4000 mm³ - 1674.6665 mm³
Unused space = 2325.3335 mm³ (rounded to four decimal places)
Therefore, the unused space in the box is approximately 2325.3 mm³.