Question

The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

The height of the cylinder is 2.67 m.

Step-by-step explanation:

• Let the height of the cylinder = h
• Internal radius of the hollow spherical shell (r) = $\dfrac{6}{2}$   = 3 cm
• external radius of the hollow spherical shell (R) = $\dfrac{10}{2}$  = 5 cm
• and the radius of the cylinder (a) = $\dfrac{14}{2}$  = 7 cm

Now, volume of the material used in hollow spherical shell = $\dfrac{4}{3}$ × π ($R^{3}$ - $r^{3}$ )

   ∴ this volume of material will be equal to the volume of the cylinder.

•      ∴    $\dfrac{4}{3}$ × π ($R^{3}$ - $r^{3}$ )  = π × $a^{2}$ × h
•                    h  = $\dfrac{4(125-27)}{147}$
•                ∴ h  = $\dfrac{8}{3}$   = 2.67 cm

So, the height of the cylinder is 2.67 m.