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Three solid spheres of a lead are melted into a single solid sphere If the radii of the three spheres are 1 cm, 6 cm and 8 cm respectively. Then radius of the new sphere is

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2 cm

3 cm

5 cm

9 cm

answer is D.

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Detailed Solution

Given that 3 solid spheres are melted into a single solid sphere such that the radii of the three spheres are 1 cm, 6 cm and 8 cm respectively.
Let

r 1, r 2, r 3

be the radii of the three sphere respectively.

∴ r 1 = 1 cm, r 2 = 6 cm, r 3 = 8 cm

The formula for the volume of sphere is given by,
Volume of a sphere

= 43 π r 3

, where r is the radius. So, after substituting the value of all the dimensions in the formula we get,
Let r be the radius of the new sphere.
Then

\frac{4}{3} π r^{3} = \frac{4}{3} π \times {(1)}^{3} + \frac{4}{3} π {\times (6)}^{3} + \frac{4}{3} π \times {(8)}^{3}

\Rightarrow \frac{4}{3} π r^{3} = \frac{4}{3} π \times [{(1)}^{3} + {(6)}^{3} + {(8)}^{3}]

{\Rightarrow r}^{3} = [1 + 216 + 512]

\Rightarrow r^{3} = 729 = {(9)}^{3}

\Rightarrow r = 9 cm

Therefore, the radius of the new sphere =9 cm.
Hence, option (4) is correct.

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