Question

4) If the diameter of a cylinder is held then find the ratio between the volume of new and the old one?​

Answer 1

$\huge{\mathtt{{\green{\boxed{\tt{\blue{\red{Ans}\gray{wer}}}}}}}}\\ Given, \\Diameter \: of \: the \: new \: cylinder: \frac{d}{2} \\ Thus, \\ Radius \: of \: the \: new \: cylinder \: = \: \frac{1}{2} x \frac{d}{2} = \frac{d}{4}\\Now, \\Volume \: of \: the \: new \: cylinder \: with \: that \: of \: the \: old \: cylinder. \\= \frac{ \frac{1}{3}\pi {r}^{2} h }{ \frac{1}{3}\pi {r}^{2}h} \\ = \frac{ \frac{1}{3}\pi (\frac{d}{ {4}})^{2}h}{ \frac{1}{3}\pi (\frac{d}{2})^{2}h} \\ \frac{ \frac{ {d}^{2} }{16} }{ { \frac{d}{4}}^{2}} \\ = \frac{4}{1} \\ =4:1 \\ \sf\orange{◆━━━━━━━▣✦▣━━━━━━━━◆}$