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 insulation purposes. How many cubic centimeters of cork dust will be required?
We have to find the volume of cork dust filled between the two vessels.
Radius of outer vessel $\left(r_{2}\right)=8 \mathrm{~cm}$
Radius of inner vessel $\left(r_{1}\right)=7 \mathrm{~cm}$
Height of the cylinder $(h)=42 \mathrm{~cm}$
So, volume of cork dust filled between the two vessels,
$=\pi h\left(r_{2}^{2}-r_{1}^{2}\right)$
$=(3.14)(42)(64-49)$
$=1978.2 \mathrm{~cm}^{2}$
$=1980 \mathrm{~cm}^{3}$
Volume of cork dust filled between the two vessels is $1980 \mathrm{~cm}^{3}$.
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