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Q.

Volume of a hollow sphere is $\frac{11352}{7} {cm}^{3} .$ If the outer radius is 8cm, find the inner radius of the sphere. (Take $π = \frac{22}{7})$ )

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a

2 cm

b

5 cm

c

4 cm

d

6 cm

answer is B.

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Detailed Solution

Given,
Volume of sphere V=

\frac{11352}{7} {cm}^{3}

Outer radius R = 8 cm
Inner radius R =?
The volume of sphere can be given as,

V = \frac{4}{3} π (R^{3} - r^{3})

\frac{11352}{7} = \frac{4}{3} \times \frac{22}{7} (8^{3} - r^{3})

\frac{11352}{7} = 512 - r^{3}

387 = 512 - r^{3}

r^{3} = 125

r^{3} = 5^{3}

So,

r = 5 cm

So, value of inner radius is 5 cm.
Correct option is 2.

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Volume of a hollow sphere is 113527 cm3.If the outer radius is 8cm, find the inner radius of the sphere. (Take π=227))