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Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively,

Question

Metallic spheres of radii 6\ cm, 8\ cm and $10 c m$ , respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

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Metallic spheres of radii 6\ cm, 8\ cm and

10 c m

, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

9 mins ago

Discuss this question LIVE

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Text solutionVerified

Given:
Radius (

r_{1}

) of first sphere

= 6

cm
Radius (

r_{2}

) of second sphere

= 8

cm
Radius (

r_{3}

) of third sphere

= 10

cm
Radius of the resulting sphere

= r

The object formed by recasting these spheres will be same in volume as the sum of the voulmes of these spheres.

So, Volume of

3

spheres = Volume of resulting shape

\frac{4}{3} π [r_{1}^{3} + r_{2}^{3} + r_{3}^{3}] = \frac{4}{3} π r^{3}

⟹ \frac{4}{3} π [6^{3} + 8^{3} + 1 0^{3}] = \frac{4}{3} π r^{3}

⟹ 216 + 512 + 1000 = r^{3}

⟹ 1728 = r^{3}

r = 12

Therefore, the radius of sphere so formed will be

12

cm.

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Question Text	Metallic spheres of radii 6\ cm, 8\ cm and $10 c m$ , respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Answer Type	Text solution:1
Upvotes	150