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Answer:
The volume of foam needed to fill the box is approximately 2926.1 cubic inches.
Step-by-step explanation:
To calculate the amount of foaming that is needed to fill the rest of the box we first need to calculate the volume of the box and the volume of the ball. Since the box is cubic it's volume is given by the formula below, while the formula for the basketball, a sphere, is also shown.
Vcube = a³
Vsphere = (4*pi*r³)/3
Where a is the side of the box and r is the radius of the box. The radius is half of the diameter. Applying the data from the problem to the expressions, we have:
Vcube = 15³ = 3375 cubic inches
Vsphere = (4*pi*(9.5/2)³)/3 = 448.921
The volume of foam there is needed to complete the box is the subtraction between the two volumes above:
Vfoam = Vcube - Vsphere = 3375 - 448.921 = 2926.079 cubic inches
The volume of foam needed to fill the box is approximately 2926.1 cubic inches.
About 2926.1 cubic inches of foam are required to completely fill the box.
What is volume?
The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.
Given data;
Diameter of the sphere,d = 9.5 in.
Side of the cube, a = 15 in.
The volume of a cube is found as;
Vcube = a³
Vcube = 15³
Vcube = 3375 cubic inches
The volume of the sphere is found as;
[tex]\rm V_{sphere} = \frac{(4\pi r^3)}{3}\\\\V_{sphere} = \frac{(4\pi (4.25)^3)}{3}\\\\V_{sphere} = 448.921 \ inch^3[/tex]
By subtracting the volume of the cube by the volume of the sphere, the number of cubic inches of packing foam required to fill the remaining space;
[tex]\rm V_{packing} = V_{cube}- V_{sphere} \\\\ \rm V_{packing} = 3375 -448.921 \\\\ V_{packing} = 2926 \ inch^3[/tex]
Hence, about 2926.1 cubic inches of foam are required to completely fill the box.
To learn more about the volume, refer to https://brainly.com/question/1578538
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