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
33.5 mm3
33.5 mm cubed
3,900 mm3
3,900 mm cubed
2,325.3 mm3
To find the volume of the marbles, we need to calculate the volume of one marble and then multiply it by the total number of marbles. The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius.
Volume of one marble = (4/3)π(2mm)³
= (4/3)π(8mm³)
= (32/3)π mm³
Volume of 50 marbles = (32/3)π mm³ * 50
= (1600/3)π mm³
≈ 523.6π mm³
≈ 1642.4 mm³
Therefore, the volume of the space occupied by the marbles is approximately 1642.4 mm³.
To find the unused space in the container, we subtract the volume of the marbles from the total volume of the container.
Unused space = Total volume - Volume of marbles
= 4000 mm³ - 1642.4 mm³
≈ 2357.6 mm³
Rounded to the nearest tenth, the unused space in the box is approximately 2357.6 mm³, which is closest to 2357.6 mm³.