The volume of a container measures 4, 000 mm? 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.
You sure ?
The volume of a sphere can be calculated using the formula V = (4/3) * π * r^3, where V is the volume and r is the radius.
Since each marble has a radius of 2 mm, the volume of each marble is:
V_marble = (4/3) * 3.14 * 2^3 = 33.49 mm^3 (rounded to two decimal places).
The total volume of the marbles in the container can be calculated by multiplying the volume of one marble by the number of marbles:
V_marbles = 33.49 mm^3/marble * 50 marbles = 1674.5 mm^3.
Finally, the space unused in the container can be determined by subtracting the volume of the marbles from the total volume of the container:
Unused space = 4000 mm^3 - 1674.5 mm^3 = 2325.5 mm^3.
Rounded to the nearest tenth, the unused space in the container is approximately 2325.5 mm^3.
Apologies for the mistake in my previous response.
To find the volume of a container, we need to multiply the length, width, and height of the container. However, in the given information, only the measurement 4,000 mm is provided, which cannot be assumed as the volume of the container. We need additional information about the dimensions of the container to accurately calculate the unused space.
To find the space unused in the box, we first need to calculate the total volume of the marbles and then subtract it from the volume of the container.
The volume of a sphere can be calculated using the formula V = (4/3) * π * r^3, where V is the volume and r is the radius of the sphere.
Given that each marble has a radius of 2 mm, we can calculate the volume of a single marble as:
V_marble = (4/3) * 3.14 * (2^3) = 33.4933 mm^3 (rounded to four decimal places).
Since there are 50 marbles in total, we can calculate the total volume of the marbles as:
V_total = 50 * V_marble = 50 * 33.4933 mm^3 = 1,674.665 mm^3 (rounded to three decimal places).
Now, we can subtract the volume of the marbles from the volume of the container to find the unused space:
Unused space = Volume of the container - Total volume of the marbles.
Given that the volume of the container is 4,000 mm^3, we can calculate the unused space as:
Unused space = 4,000 mm^3 - 1,674.665 mm^3 = 2,325.335 mm^3 (rounded to three decimal places).
Therefore, the space in the box that is unused is approximately 2,325.335 mm^3.