Answer:
103 cube inches
Step-by-step explanation:
Since sphere fits snugly inside a cube therefore diameter of sphere will be equal to side of the cube [ which is given to be 6 inches ]
diameter = 6 inches
radius = [tex]\frac{diameter }{2}[/tex]
= [tex]\frac{6 }{2}[/tex]
= 3 inches
Volume of the sphere is given by [tex]\frac{4}{3}\pi r^3[/tex]
here r =3 inches
therefore volume is= [tex]\frac{4}{3}\pi 3^3[/tex]
= 36 pi
= 36 ( 3.142)
= 113.097 cube inches
Volume of Cube = side x side xside = 6x6x6 = 216 cube inches
Volume of space between sphere and cube = 216 - 113.097= 102.9 cube inches , nearest whole number is 103 cube inches
