A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symme

1.	A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16 cm 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 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 = π(r₂²– r₁²) x h = π(8²– 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.

A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16 cm 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 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 = π(r₂²– r₁²) x h

= π(8²– 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.