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The weight of a metallic spherical shell is 11.176 kg. If the inner radius of the cell is 6 cm. 1 cm3 of the metal weights 21 g then what is the thickness of the shell?
- a)1 cm
- b)2 cm
- c)3 cm
- d)4 cm
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The weight of a metallic spherical shell is 11.176 kg. If the inner ra...
To find the thickness of the metallic spherical shell, we need to use the concept of density and weight.
Given data:
- Weight of the metallic spherical shell = 11.176 kg
- Inner radius of the shell = 6 cm
- Density of the metal = 21 g/cm3
Let's solve the problem step by step:
1. Calculate the volume of the spherical shell:
The volume of a spherical shell can be calculated using the formula:
Volume = (4/3) * π * (R_outer^3 - R_inner^3)
Since the inner radius is given as 6 cm, we can assume the outer radius as R cm.
Volume = (4/3) * π * (R^3 - 6^3)
2. Calculate the weight of the metallic shell:
The weight of the metallic shell can be calculated using the formula:
Weight = Volume * Density
11.176 kg = Volume * 21 g/cm3
Now, let's convert the weight to grams:
11.176 kg = 11176 g
Therefore, Volume = 11176 g / 21 g/cm3
3. Substitute the value of Volume in the equation calculated in step 1 and solve for R:
11176 g / 21 g/cm3 = (4/3) * π * (R^3 - 6^3)
4. Simplify the equation:
(11176 g / 21 g/cm3) = (4/3) * π * (R^3 - 216)
5. Solve for R:
R^3 - 216 = (11176 g / 21 g/cm3) * (3/4π)
R^3 - 216 = 1596 g / 7 g/cm3
6. Simplify and solve for R:
R^3 = (1596 g / 7 g/cm3) + 216
R^3 = 228 g/cm3
Taking the cube root on both sides, we get:
R ≈ 6.2 cm
7. Calculate the thickness of the shell:
Thickness = R_outer - R_inner
Thickness = 6.2 cm - 6 cm
Thickness ≈ 0.2 cm
Therefore, the thickness of the metallic spherical shell is approximately 0.2 cm.
Given data:
- Weight of the metallic spherical shell = 11.176 kg
- Inner radius of the shell = 6 cm
- Density of the metal = 21 g/cm3
Let's solve the problem step by step:
1. Calculate the volume of the spherical shell:
The volume of a spherical shell can be calculated using the formula:
Volume = (4/3) * π * (R_outer^3 - R_inner^3)
Since the inner radius is given as 6 cm, we can assume the outer radius as R cm.
Volume = (4/3) * π * (R^3 - 6^3)
2. Calculate the weight of the metallic shell:
The weight of the metallic shell can be calculated using the formula:
Weight = Volume * Density
11.176 kg = Volume * 21 g/cm3
Now, let's convert the weight to grams:
11.176 kg = 11176 g
Therefore, Volume = 11176 g / 21 g/cm3
3. Substitute the value of Volume in the equation calculated in step 1 and solve for R:
11176 g / 21 g/cm3 = (4/3) * π * (R^3 - 6^3)
4. Simplify the equation:
(11176 g / 21 g/cm3) = (4/3) * π * (R^3 - 216)
5. Solve for R:
R^3 - 216 = (11176 g / 21 g/cm3) * (3/4π)
R^3 - 216 = 1596 g / 7 g/cm3
6. Simplify and solve for R:
R^3 = (1596 g / 7 g/cm3) + 216
R^3 = 228 g/cm3
Taking the cube root on both sides, we get:
R ≈ 6.2 cm
7. Calculate the thickness of the shell:
Thickness = R_outer - R_inner
Thickness = 6.2 cm - 6 cm
Thickness ≈ 0.2 cm
Therefore, the thickness of the metallic spherical shell is approximately 0.2 cm.
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Community Answer
The weight of a metallic spherical shell is 11.176 kg. If the inner ra...
Let the thickness of the shell be t.
Inner radius = r, outer radius = R
∴ Volume of spherical shell = 4/3 π(R3 - r3)
∴ Weight of spherical shell
= 11.1786 kg
⇒ R3 = 343 ⇒ R = 7 cm
∴ Thickness = t = (R - r) = (7 - 6) = 1 cm
Inner radius = r, outer radius = R
∴ Volume of spherical shell = 4/3 π(R3 - r3)
∴ Weight of spherical shell
= 11.1786 kg
⇒ R3 = 343 ⇒ R = 7 cm
∴ Thickness = t = (R - r) = (7 - 6) = 1 cm
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