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A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form of a cone of base diameter 8cm. What is the height of the cone?

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answer is B.

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Detailed Solution

Given that a metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively.
Diameter of cone = 8cm.
Determining the volume of spherical shell with internal diameter,

d i = 4

cm and external diameter,

d o = 8

cm.

Volumeofspherical shell = 4 π 3 d o 2 3 − d i 2 3 ⇒ 4 π 3 43 − 23 ⇒ 4 π 3 64 − 8 ⇒ 224 π 3

Assuming the height of the cone to be h. The volume of the cone is

V = π d 2 h 12

, where d is the diameter of the cone.
Substitute

224 π 3

for V and 8 for d in the formula

V = π d 2 h 12

to obtain the height of the cone.

224 π 3 = π 82 h 12 224312 = 64 h 89664 = h 14 = h

Therefore, option 2 is correct.

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