We are asked to find the volume of the empty space in the box. To do so, we need to subtract the volume of the three tennis balls from the volume of the box. We will start by finding the volume of the box, which is in the shape of the following rectangular prism.
Recall that the volume of a rectangular prism with length l, width w, and height h can be calculated using the following formula.
V=l w hIn this case, we are given that l= 12.1, w= 3.5, and h= 3.5, so we have enough information to calculate the volume of the rectangular prism.
Therefore, the volume of the box is 148.225 cm^3. Next, we will calculate the volume of the balls. To find the volume of each ball, recall that the volume of a sphere is equal to four thirds the product of π and the cube of the radius r.
V=4/3Ï€ r^3
In this case, we are given that the diameter is 3.3 centimeters. To find the radius, we can divide the diameter d by 2.
We got that the volume of each ball is about 18.8 cm^3. Finally, we can calculate the volume of the empty space by subtracting the volume of three balls from the volume of the box.
148.225-3(18.8)= 91.825 ≈ 91.8
Therefore, the volume of the empty space in the box is about 91.8 cm^3.
