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A sphere of radius 2 cm is put inside a hollow sphere of outer radius 10 cm. If the inner volume of the hollow sphere is 76π/3 cm3, find the inner radius of the hollow sphere.
  • a)
    9.9 cm
  • b)
    9 cm
  • c)
    3 cm
  • d)
    7.9 cm
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A sphere of radius 2 cm is put inside a hollow sphere of outer radius ...
The inner volume of the hollow sphere can be calculated by subtracting the volume of the small sphere from the volume of the large sphere.

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius.

The volume of the small sphere is V1 = (4/3)π(2^3) = (4/3)π(8) = (32/3)π.

The volume of the large sphere is V2 = (4/3)π(10^3) = (4/3)π(1000) = (4000/3)π.

The inner volume of the hollow sphere is V2 - V1 = (4000/3)π - (32/3)π = (3968/3)π.

Given that the inner volume of the hollow sphere is 76, we can set up the equation:

(3968/3)π = 76.

Dividing both sides of the equation by (3968/3)π gives:

76 / ((3968/3)π) = 1.

Therefore, the inner volume of the hollow sphere is 1.
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Community Answer
A sphere of radius 2 cm is put inside a hollow sphere of outer radius ...
R = 10 cm, r = r cm
Volume of hollow sphere =  (R3 - r3)
[(10)3 - r3]
= 1,000 - r3
r3 = 1,000 - 19 = 981
r = (981)1/3 = 9.9
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A sphere of radius 2 cm is put inside a hollow sphere of outer radius 10 cm. If the inner volume of the hollow sphere is 76π/3 cm3, find the inner radius of the hollow sphere.a)9.9 cmb)9 cmc)3 cmd)7.9 cmCorrect answer is option 'A'. Can you explain this answer?
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