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

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Solution

Let $R$ and $r$ be the outer and inner radii of the hollow sphere respectively.
Let $V$ be the volume of the hollow sphere.
Now, given that $V = \frac{11352}{7} {c m}^{3}$
$\Rightarrow \frac{4}{3} π (R^{3} - r^{3}) = \frac{11352}{7}$
$\Rightarrow \frac{4}{3} \times \frac{22}{7} (8^{3} - r^{3}) = \frac{11352}{7}$
$512 - r^{3} = 387 \Rightarrow r^{3} = 125 = 5^{3}$
Hence, the inner radius, $r = 5 c m$ .

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

Let R and r be the outer and inner radii of the hollow sphere respectively.Let V be the volume of the hollow sphere.Now, given that V=113527cm3⇒43π(R3−r3)=113527⇒43×227(83−r3)=113527512−r3=387⇒r3=125=53Hence, the inner radius, r=5cm.

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