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If Three Metallic Spheres of Radii 6 Cm, 8 Cm and 10 Cm Are Melted to Form a Single Sphere, the Diameter of the Sphere is - Mathematics

MCQ

If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the sphere is

Options

  • 12 cm

  •  24 cm

  •  30 cm

  • 36 cm

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Solution

Let r be the radius of single sphere.

Now,

The volume of single sphere = sum of volume of three spheres

`4/3pir^3 = 4/3pi(61)^3 + 4/3 pi(8)^3 + 4/3 pi(10)^3`

`4/3pir^3 = 4/3 pi(216 + 512 + 1000)`

       `r^3 = 1728`

         `r = 12 cm`

Hence, the diameter = 20 × r = 24 cm

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Q 21 | Page 89
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