Question

A museum has two spherical cannonballs on display. Each cannonball is made of a type of iron that weighs about 463 pounds per cubic foot. a. The diameter of the smaller cannonball is 1 inch less than the diameter of the larger cannonball. Can you determine how much less the smaller cannonball weighs than the larger cannonball

Answer 1

the smaller cannonball weighs 88.94% less than the bigger cannonball.

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.