Question

What length of the solid cylinder that is $2$ cm in diameter must be taken to cast into a hollow cylinder of external diameter $12$ cm, $0.25$ cm thick, and $15$ cm long?

• A. $44.0123$ cm
• B. $42.3215$ cm
• C. $44.0625$ cm
• D. $44.6023$ cm

Answer 1

The correct option is C $44.0625$ cm

Volume of hollow cylinder $=\pi h(R_o^2-R_i^2)$

Here, $R_o=\frac{12}{2}=6cm$ and $R_i=(6-0.25)cm$

Volume of solid cylinder $=\pi r^{2}h$ {Where $r=\frac{2}{2}=1cm$}

The volume of solid cylinder$=$Volume of the hollow cylinder

$\Rightarrow \pi r^{2}h=\pi ({\left(6\right)}^2-{(6-0.25)}^2)\times 15$

$\Rightarrow {\left(1\right)}^2\times h=(36-33.0625)\times 15$

$h=44.0625cm$

$\therefore$ Length of solid cylinder$=44.0625cm$