The thickness of the walls of each hollow lump of iron ore is: 0.295cm. This is determined using the knowledge of the Volume of a Hollow Sphere.
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What is the Volume of a Hollow Sphere?</h3>
The formula for the Volume of a Hollow Sphere is give as:
Volume of a Hollow = 4/3 R³ – 4/3 r³
Step 1 - Find the apparent volume of 8cm diameter sphere including the wall the the hollow inside
V = 4/3 r³
V = (4/3) (8)³
V = (4/3) * (22/7) * 512
V = 2145.52cm³
Step 2 - Determine the mass of Gold required for the sphere to achieve the density of iron ore if the apparent volume is as given in Step 1 above.
Recall that Mass = Density * Volume
Mass = 5.15 * 2145.52
Mass = 11049.45
Step 3 - Find volume of gold based on mass calculated in Step 2 above
Recall that :
Volume = Mass/Density
Thus,
V = 11049.4/19.3
Thus, Volume = 572.51cm³
Step 4 - Find the width of the wall of a hollow sphere for the volume realized in step 3
Recall the initial formula:
Volume of a Hollow = 4/3 R³ – 4/3 r³
Thus, 572.51 = (4/3) (8³ - (8 - t)³)
572.51 = (4/3) *(22.7) *(8³ - (8 - t)³)
572.51 = (88/21) *(8³ - (8 - t)³)
Multiply both sides by 21 and we have
88 (512 - (8 - t)³) = 12,022.71
Simplify further
(8 - t)³ = 357.38
t = 0.9035cm
Learn more about Volume of a Hollow Sphere at:
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