A ball is placed into a cubed box base 30 inches height 36 inches
Find the difference in space from the sphere and the box. Use 3.14 for π.
To find the volume of the sphere, we use the formula V = (4/3)πr^3, where r is the radius of the sphere. Since the diameter of the sphere is equal to the edge of the box (30 inches), the radius is 15 inches.
V_sphere = (4/3)(3.14)(15^3)
V_sphere = (4/3)(3.14)(3375)
V_sphere = 14130 cubic inches
The volume of the box is simply the volume of a cube, V_box = side^3 = 30^3 = 27000 cubic inches.
Now we find the difference in space between the sphere and the box:
Difference = |V_sphere - V_box|
Difference = |14130 - 27000|
Difference = 12870 cubic inches
Therefore, the difference in space between the sphere and the box is 12870 cubic inches.