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What will be the number of solid spheres, each of diameter 6 cm, that can be made by melting a solid metal cylinder of height 45 cm and diameter 4cm?

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Detailed Solution

We have to find the number of solid spheres, each of diameter 6 cm, that can be made by melting a solid metal cylinder of height 45 cm and diameter 4cm.
Volume of a cylinder

= π r 2 h

,where

r

is radius, and

h

is height.
Calculating the volume of cylinder,
Note that,

h = 45 c m, r = 2 c m

= π r 2 h = π × 22 × 45 = 565.48 c m 3

Calculating the number of a solid sphere,
Volume of one sphere,

= 43 π r 3 = 43 × π × 33 = 113.1 c m 3

So, the number of a solid sphere,

= 565.48 113.1 = 5

Thus, the number of the solid spheres is 5.
Therefore, option 3 is correct.

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