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Question -

A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16cm and height of 42 cm. The total space between the two vessels is filled with cork dust for heat insulation purposes. How many cubic cms of the cork dust will be required?



Answer -

Given,

Depth of the cylindricalvessel = Height of the cylindrical vessel = h = 42 cm (common for both)

Inner diameter of thecylindrical vessel = 14 cm

So, the inner radiusof the cylindrical vessel = r= 14/2 = 7 cm

Outer diameter of thecylindrical vessel = 16 cm

So, the outer radiusof the cylindrical vessel = r= 16/2 = 8 cm

Now,

The volume of thecylindrical vessel

V = π(r22 –r12 ) x h

= π(82 –72 ) x 42

= 22/7 x 15 x 42

V = 1980 cm3

Therefore, the totalspace between the two vessels is 1980 cm3, which is also the amountof cork dust required.

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