Final answer:
To fill the room, you'd need approximately 291,919 racquetballs. Calculated by dividing the room's volume (5,760 cubic feet) by the volume of one racquetball (0.0198 cubic feet).
Step-by-step explanation:
To find out how many racquet balls it would take to fill the room, we need to calculate the volume of the room and then divide it by the volume of one racquetball. The volume of the room is determined by multiplying its width, length, and height: 20 ft x 32 ft x 9 ft = 5,760 cubic feet. The volume of one racquetball can be calculated using its diameter: 2.25 in (or 0.1875 ft, since there are 12 inches in a foot) and the formula for the volume of a sphere: (4/3) x pi x (radius)^3. In this case, the radius is half the diameter, so it is 0.09375 ft. Now, we can find the volume of one racquetball: (4/3) x 3.14 x (0.09375 ft)^3 = 0.0198 cubic feet. Finally, we can divide the volume of the room by the volume of one racquetball to find the number of racquetballs needed: 5,760 cubic feet / 0.0198 cubic feet = 291,919 racquetballs.