Question 44

A hollow sphere is melted to form small identical! hollow spheres. Inner and outer radius of the bigger sphere are 4 cm and 6 cm respectively. If inner and outer radii of the smaller sphere are 2 cm and 3 cm respectively, then how many smaller spheres can be formed?

Solution

Let say, n number of sphere can be made.

So,According to question,

$$\frac{4}{3}\pi\left(R^3-r^3\right)=n\times\frac{4}{3}\pi\left(R_1^3-r_1^3\right).$$

or, $$\frac{4}{3}\pi\left(6^3-4^3\right)=n\times\frac{4}{3}\pi\left(3^3-2^3\right).$$

or, $$\left(216-64\right)=n\times\left(27-8\right).$$

or, $$n=\frac{152}{19}=8.$$

B is correct choice.

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