Answer:
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
