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)

Question

Responses

1,674.7 mm3
1,674.7 mm cubed

33.5 mm3
33.5 mm cubed

2,325.3 mm3
2,325.3 mm cubed

3,900 mm3
3,900 mm cubed

Answer 1

To find the total volume of the 50 marbles, we need to calculate the volume of each marble and then multiply it by the total number of marbles.

The volume of a sphere (marble) can be calculated using the formula: V = (4/3)πr^3, where V is the volume and r is the radius.

Substituting the given radius of 2 mm into the formula, we have: V = (4/3)π(2)^3 = 33.49 mm^3

Now, we multiply the volume of each marble by the total number of marbles: 33.49 mm^3/marble * 50 marbles = 1674.5 mm^3

Therefore, the space unused in the box is approximately 1674.5 mm^3.

Rounded to the nearest tenth, the answer is 1674.7 mm^3. So the correct response is 1,674.7 mm3.