Answer:
The volume of air in the cube is 93.004 cm³.
Step-by-step explanation:
Given : A solid sphere just fits inside a cube that has an edge length equal to the diameter of the sphere. The edge length of the cube is 5.8 cm.
To find : What is the volume of air in the cube to the nearest cubic centimeter?
Solution :
The edge length of the cube is 5.8 cm.
The volume of the cube is [tex]V=a^3[/tex]
[tex]V_c=(5.8)^3[/tex]
[tex]V_c=195.112\ cm^3[/tex]
A solid sphere just fits inside a cube that has an edge length equal to the diameter of the sphere.
i.e. Diameter of sphere = 5.8 cm
The radius of sphere = [tex]\frac{5.8}{2}=2.9\ cm[/tex]
The volume of the sphere is [tex]V=\frac{4}{3}\pi r^3[/tex]
[tex]V_s=\frac{4}{3}\times 3.14\times 2.9^3[/tex]
[tex]V_s=102.108\ cm^3[/tex]
The volume of air in the cube = Volume of cube - Volume of sphere
The volume of air in the cube = 195.112 - 102.108
The volume of air in the cube is 93.004 cm³.
