Question

the radii of two cylindrical vessels are in the ratio of 1:3 and their heights are in the ratio of 1:2 .the ratio of their volumes is​

Answer 1

Answer:

1:18 is the correct answer.

Answer 2

$\begin{gathered}\dag\:\underline{\sf AnswEr :} \\ \end{gathered}$

• Ratio of radii of two cylindrical vessels = 1:3
• Ratio of heights of two cylindrical vessels = 1:2
• The ratio of their volumes = ?
• Let the radius of first cylinder be r.
• Let the radius of second cylinder be r'.
• Let the height of first cylinder be h.
• Let the height of second cylinder be h'
• Formula of volume of cylinder is πr²h

$\begin{gathered}\bigstar\:\underline{\textbf{According to the Question Now :}} \\ \end{gathered}$

$\begin{gathered}:\implies\sf \dfrac{Volume \: of \: 1^{st} \: cylinder}{Volume \: of \: 2^{nd} \: cylinder} = \dfrac{\pi r^2h}{\pi r'^2 h'} \\ \end{gathered}$

$\begin{gathered}:\implies\sf \dfrac{Volume \: of \: 1^{st} \: cylinder}{Volume \: of \: 2^{nd} \: cylinder} = \dfrac{\pi \times (1)^{2} \times 1}{\pi \times (3)^2 \times 2} \\ \end{gathered}$

$\begin{gathered}:\implies\sf \dfrac{Volume \: of \: 1^{st} \: cylinder}{Volume \: of \: 2^{nd} \: cylinder} = \dfrac{\pi \times 1\times 1}{\pi \times 9 \times 2} \\ \end{gathered}$

$\begin{gathered}:\implies\sf \dfrac{Volume \: of \: 1^{st} \: cylinder}{Volume \: of \: 2^{nd} \: cylinder} = \dfrac{1\times 1}{ 9 \times 2} \\ \end{gathered}$

$\begin{gathered}:\implies \underline{ \boxed{\textsf{ \textbf{ \dfrac{ \text {Volume} \: \text{ of }\: \text 1^{ \text{st}} \: \text{cylinder}}{ \text{Volume} \: \text{of} \: \text2^{ \text{nd}} \: \text{cylinder}} = \dfrac{ \text1}{ \text{18}} }}}}\\ \end{gathered}$

$\large \bold{@WildCat7083}$