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Eight solid spheres of the same size are made by melting a solid metallic cylinder of base diameter $6 cm$ and height $32 cm$ . Then, what is the diameter of each sphere?

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5cm

3cm

6cm

8cm

answer is C.

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Detailed Solution

Given are eight solid spheres of the same size and a solid metallic cylinder of base diameter

6 cm

and height

32 cm

.
We have the following formulae,
Volume of sphere =

43 π r 3

Volume of cylinder =

= π r 2 h

Then,
Radius of sphere

r s = ?

Radius of cylinder

r c y = 3 cm

Height of cylinder

h c y = 32 cm

Volume of 8 spheres = volume of cylinder

8 × 43 π r s 3 = π r c y 2 h c y 8 × 43 × r s 3 = 32 × 32 v s 3 = 33 ⇒ r s = 3 c m

Diameter of the sphere will be,

= 2 × 3 = 6 c m

Thus, the diameter of the sphere is 6cm.
Therefore the correct option is 3.

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