Question

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

Answer 1

Solution:

As per the parameters given in the question, we have

Depth of the cylindrical vessel = Height of the cylindrical vessel = h = 42 cm

Inner diameter of the cylindrical vessel = 14 cm

Inner radius of the cylindrical vessel = r₁ =$\frac{14}{2}$ = 7 cm ( as we know that the radius is half of the diameter )

Outer diameter of the cylindrical vessel = 16 cm

Outer radius of the cylindrical vessel = r₂ = $\frac{16}{2}$ = 8 cm ( as we know that the radius is half of the diameter )

Now,

The volume of the cylindrical vessel $=\pi \times (r_2^2-r_1^2)\times h$

$=\pi \times (8^2-7^2)\times 42=1980c{m}^3$

Therefore, Volume of the vessel = V = 1980 cm³ = Amount of cork dust required.