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# 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?

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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.

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1. 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.

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