A metallic cubiod of dimension $22 c m . \times 15 c m \times 7 .5 c m,$ was melted and cast into a cylinder of height $14 c m .$ What is its radius?

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Solution

$\begin{matrix} D i m e n s i o n s o f m e t a l c u b o i d l e n g t h l = 22 c m B r e a d t h b = 15 c m a n d H e i g h t h = 7.5 c m a n d H e i g h t o f c y l i n d e r (H) = 14 c m L e t r a d i u s o f t h e c y l i n d e r b e^{'} r^{'} c m N o w, v o l u m e o f c y l i ln d e r = v o l u m e o f t h e m e t a l c u b o i d π r^{2} H = l b h \frac{22}{7} \times r^{2} \times 14 = 22 \times 15 \times 7.5 r^{2} = \frac{22 \times 15 \times 7.5 \times 7}{22 \times 14} r = \frac{15}{2} ∴ r = 7.5 c m H e n c e, T h e r a d i u s o f c y l i n d e r r = 7.5 c m . \end{matrix}$

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