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

• 12 cm

•  24 cm

•  30 cm

• 36 cm

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

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APPEARS IN

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