Volume of Spheres Quick Check
4 of 54 of 5 Items
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
2,325.3 mm3
2,325.3 mm cubed
3,900 mm3
3,900 mm cubed
33.5 mm3
33.5 mm cubed
1,674.7 mm3
To find the total volume of the marbles, we first need to find the volume of each marble and then multiply by the total number of marbles:
Volume of each marble = (4/3) x pi x (2mm)^3
Volume of each marble = (4/3) x 3.14 x 8
Volume of each marble = 33.4933 mm^3 (approx)
Total volume of all marbles = 33.4933 mm^3/marble x 50 marbles
Total volume of all marbles = 1674.7 mm^3
The volume of the container is 4000 mm^3, so the space unused in the box is:
4000 mm^3 - 1674.7 mm^3 = 2325.3 mm^3
Therefore, the space unused in the box is 2,325.3 mm^3. The correct answer is:
2,325.3 mm3