Question

A cylindrical vessel of diameter $16cm$ and height $h$ cm is fixed symmetrically inside a similar vessel of diameter $20cm$ and height $h$ cm. The total space between the two vessels is filled with cork dust. How many cubic centimeters of cork dust is used?

• A. $72\pi hc{m}^3$
• B. $36\pi hc{m}^3$
• C. $18\pi hc{m}^3$
• D. $12\pi hc{m}^3$

Answer 1

The correct option is B $36\pi hc{m}^3$

Volume of cork dust used $=$ Volume of the outer cylindrical vessel $-$ Volume of inner cylindrical vessel

Volume of a Cylinder of Radius "R" and height "h" $=\pi R^{2}h$

Radius of the inner cylindrical vessel $=\frac{16}{2}=8cm$

Radius of the outer cylindrical vessel $=\frac{20}{2}=10cm$

Hence, Volume of cork dust used $=\pi {10}^{2}h-\pi 8^{2}h=36\pi h{cm}^3$