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Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. What is the diameter of the sphere?

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2cm

3cm

4cm

5cm

answer is A.

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Detailed Solution

Given that,
The volume of cylinder with diameter

2 V = 13 π r 2 h 2 V = 13 π 32 h 1 V = 96 π h 1 V = 32 π h 1 … … 1

cm.
And height

= 16

cm.
The volume of the closed body determines the capacity or amount of liquid that can be stored in the body within its boundary.

Volume of cylinder = π d 2 2 h ⇒ π 22216 ⇒ 16 π

Assume the radius of the sphere is r.
The volume of the sphere is

V = 4 π r 3 3

and volume of 12 spheres is

V = 12 4 π r 3 3

⇒ 16 π = 12 4 π r 3 3 ⇒ r 3 = 1 ⇒ r = 1

The diameter of the sphere is

= 16

cm.
Therefore, option 1 is correct.

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