Answer:
the smaller cannonball weighs 88.94% less than the bigger cannonball.
Step-by-step explanation:
The volume of bigger spherical cannonball is given by
Vb = (4/3)π(db/2)³
Vb = (4/3)πdb³/8
Vb = (1/6)πdb³
we know that mass is density into volume
m = DV
m = (1/6)πdb³*463
suppose the mass of bigger cannonball is 1 pound
1 = (1/6)πdb³*463
db³ = 6/463*π
db = ∛6/(463*π)
db = 0.160 ft
the diameter of smaller cannonball is 1 inch less than the diameter of the larger cannonball.
1 inch = 0.0833 foot
ds = db - 0.0833
ds = 0.160 - 0.0833
ds = 0.077 ft
The volume of smaller cannonball is
Vs = (4/3)π(ds/2)³
Vs = (4/3)π(0.077/2)³
Vs = 0.000239
The mass of smaller cannonball is
m = DV
m = 463*0.000239
m = 0.1106 lb
Difference in mass
difference = (1 - 0.1106/1)*100
difference = 88.94%
Therefore, the smaller cannonball weighs 88.94% less than the bigger cannonball.
