Question

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 4 cm is
(a)3
(b)5
(c)4
(d)6

Answer 1

Answer:

The number of solid spheres is 5

Among the given options option (b) 5 is  the correct answer.

Step-by-step explanation:

Given :  

Height of a solid cylinder, h = 45 cm

Diameter of solid sphere = 6 cm

Diameter of a solid cylinder = 4 cm  

Radius of solid sphere ,R  = 6/2 = 3 cm

Radius of a solid cylinder , r = 4/2 = 2 cm  

 

Let 'n’ be the number of solid spheres  

Volume of Cylinder = n × Volume of sphere

n = Volume of Cylinder / Volume of sphere

n = (πr²h) /(4/3πR³)

n = (R²h) /(4/3r³)

n = (2² × 45)/ 4/3 × 3³

n = (4 × 45)/(4 × 27/3)

n = 45 /( 9)

n = 5  

Number of solid spheres = 5  

Hence, the number of solid spheres is 5  

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Answer 2

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