Question

A cylindrical pencil of diameter $1.2cm$ has one of its ends sharped into a conical shape of height $1.4cm$. The volume of the material removed is (in cub. cms)..........

• A. $4.224$
• B. $1.056$
• C. $10.56$
• D. $42.24$

Answer 1

Answer: (B)

$1.056$

Let us consider only the section of the pencil, which was sharpened.
As the height of the conical part is $1.4cm$, height of the cylindrical part which was originally there is also $h=1.4cm$ and radius of the cylindrical part $=\frac{Diameter}{2}=\frac{1.2}{2}=0.6cm$
Now, Volume of the material removed $=$ Volume of cylindrical section $-$ Volume of conical shape formed after sharpening
So, Volume of the material removed $=\pi r^{2}h-\frac{1}{3}\pi r^{2}h=\frac{2}{3}\pi r^{2}h=\frac{2}{3}\times \frac{22}{7}\times {0.6}^2\times 1.4=1.056{cm}^3$
Hence, option 'B' is correct.