A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm3 and that of water is 1000 kg/m3. A) 37 cm B) 6.6 cm C) 79 cm D) 131 cm

B) 6.6 cm

Explanation:

A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm3 and that of water is 1000 kg/m3. A) 37 cm B) 6.6 cm C) 79 cm D) 131 cm

density steel 7750 to 8050 kg/m³, use 7870

density of water at 20C = 0.998 g/cm³ = 998 kg/m³

Note, the overall density must be equal to that of water, 998 kg/m³

density is the ratio of mass of a body to its volume

volume = V = ⁴/₃πr³ = ⁴/₃π (1.5) ³ = 14.14 m³

Mass = 998 kg/m³ x 14.14 m³ = 14109 kg

Density of steel = 7870 kg/m³ = 14109 kg / V

V = 1.79 m³

deduct 1.79 m³ from the total volume of 14.14 m³

Volume of shell is ⁴/₃πr1³ - ⁴/₃πr2³ = ⁴/₃π (r1³ - r2³) = 1.79

divide ⁴/₃π from both sides

r1³ - r2³ = 0.428 m³

r2³ = (1.5) ³ - 0.428

r2 = 1.434

to get the thickness we say that

the radius of the hollow steel ball - the radius of the ball

Thickness is 1.5 - 1.434 = 0.066 m or 6.6 cm