a spherical metallic shell with 10cm exrenal diameter weighs 1789*1/3g . find the thickness of the shell if the density isd 7g/cm cube.
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density = mass/volume
weight = 1789 1/3 =5368/3 gm
volume = 5368/(3×7) cm³
now,
Let external radius = R = 10 cm
internal radius = r
volume of the material = external volume - internal volume
= (4/3)π (R³ - r³)
(4/3)π (R³ - r³)= 5368/(3×7) cm³
⇒10³ - r³ = 61
⇒r³ = 1000 -61
⇒r³ =939
⇒r =∛939 = 9.792 cm
so thickness of the shell = 10 - 9.792 = 0.208 cm
weight = 1789 1/3 =5368/3 gm
volume = 5368/(3×7) cm³
now,
Let external radius = R = 10 cm
internal radius = r
volume of the material = external volume - internal volume
= (4/3)π (R³ - r³)
(4/3)π (R³ - r³)= 5368/(3×7) cm³
⇒10³ - r³ = 61
⇒r³ = 1000 -61
⇒r³ =939
⇒r =∛939 = 9.792 cm
so thickness of the shell = 10 - 9.792 = 0.208 cm
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