In this question we have to find the amount of cork

dust required given that 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.

This question is from r d sharma class 10 maths.

I found this question while doing mensuration of

class 10.

I need help in getting the solution.

Given,

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

Inner diameter of the cylindrical vessel = 14 cm

So, the inner radius of the cylindrical vessel = r1 = 14/2 = 7 cm

Outer diameter of the cylindrical vessel = 16 cm

So, the outer radius of the cylindrical vessel = r2 = 16/2 = 8 cm

Now,

The volume of the cylindrical vessel

V = Ï€(r22 â€“ r12 ) x h

= Ï€(82 â€“ 72 ) x 42

= 22/7 x 15 x 42

V = 1980 cm3

Therefore, the total space between the two vessels is 1980 cm3, which is also the amount of cork dust required.