Answer:
To find the percentage of space in the crate that is empty, we first need to calculate the total volume of the crate and the volume of the cylinders.
The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
Given that the radius of each cylinder is 4cm and the height of each cylinder is 14cm, we can calculate the volume of one cylinder as follows:
V_cylinder = π * (4cm)^2 * 14cm = 704π cm^3
Since there are 6 cylinders in the crate, the total volume of the cylinders is:
V_total_cylinders = 6 * 704π cm^3 = 4224π cm^3
The total volume of the crate can be calculated by multiplying the base area (πr^2) of the crate by its height (14cm):
V_crate = π * (4cm)^2 * 14cm = 224π cm^3
To find the percentage of space in the crate that is empty, we need to calculate the volume of the empty space. We can do this by subtracting the volume of the cylinders from the total volume of the crate:
V_empty_space = V_crate - V_total_cylinders = 224π cm^3 - 4224π cm^3 = -4000π cm^3
Since the volume of the empty space is negative, this means that the cylinders are occupying more space than the crate can hold. In other words, there is no empty space in the crate.
Therefore, the percentage of space in the crate that is empty is 0%.
Explanation: