Answer:
Step-by-step explanation:
We are given diameter of the ball in the empty box = 2.9 inches.
So, the each side of the box is 2.9 inches.
Radius of the ball = 2.9/2 = 1.45 inches.
Volume of the complete box without ball =[tex](Side)^3[/tex].
Plugging value of side in above formula, we get
Volume of the empty box = [tex](2.9)^3.[/tex]=24.389 cubic inches.
Volume of the ball = volume of the sphere with radius 1.45 inches = [tex]\frac{4}{3} \pi r^3[/tex].
= [tex]\frac{4}{3} \pi (1.45)^3[/tex] =[tex]\frac{12.1945\pi }{3}[/tex]
= 12.77.
Therefore, volume of the empty box around the ball = Volume of box-volume of ball = 24.389 - 12.77 = 11.619 cubic inches.
