To find the number of whole ping-pong balls that would fit into an average school bus, we first need to find the volume of both an average school bus and a ping pong ball.

A standard ping-pong ball has a radius of 2cm. To find its actual volume we would use the formula for volume of a sphere - v = 4/3*pi*r^3

• Actual volume of a ping-pong ball = 4/3*pi*(2*2*2) = 33.5103216 cubic cm

Unfortunatly if we were to use this value to find the number of ping-pong balls that could fit into a school bus we would not be accounting for the empty space surrounding a sphere when stacked with other spheres. To get a more accurate count we can treat the ping-pong ball as a cube and say that we are stacking the ping-pong balls directly on top of each other.

To find its cubed volume we multiply its length by its width by its height. Due to the ping-pong ball being sphereical each of these dimension are equal to its diameter.

• Volume of the ball = 4cm*4cm*4cm = 64 cubic cm.

An average school bus is 37' long, 8' wide and 10' tall.

• Volume of a school bus = 37'x8'x10' = 2960 cubic feet.

To use these measurments we must first convert cubic feet to cubic cm.

• 2960 cubic feet = 83,817,865.9 cubic cm

Last, we divide the volume of the school bus by the volume of the ping-pong ball.

• 83,817,865.9 / 64 rounded down = 1,309,654 ping pong balls

This number assumes that the ping-pong balls are stacked directly on top of each other rather than staggered. Staggering the ping-pong balls would increase the count. Also this ignores the fact that we want the pingpong balls stay whole and not be cut into smaller pieces to fit within the dimensions. To fix this lets see how many complete balls can fit in each dimension.

Bus length = 37' = 1127.76 cm
# of balls = 1127.76/4 rounded down = 281 balls

Bus width = 8' = 243.84 cm
# of balls = 243.84/4 rounded down = 60 balls

Bus height = 8' = 304.8 cm
# of balls = 304.8/4 rounded down = 76 balls

Total balls = 281*60*76 = 1,281,360 complete ping-pong balls

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