Question

*If the ratio of the volumes of two cylinders of equal height is 25:36, what is the ratio of their radii?*​

Answer 1

$\Large{\underline{\sf{Given:}}}$

• Ratio of Volumes of two Cylinders = 25:36
• Height of the cylinders are equal

$\Large{\underline{\sf{To\;Find:}}}$

• Ratio of 'Radii' the cylinders

$\huge{\underline{\underline{\bf{࿇\;Solution:}}}}$

◯ Let's Radius of the cylinder be r and heights be h then volumes of the cylinders are $\bf{V_1 , V_2}$

$❉\;{\boxed{\underline{\sf{Volume_{(cylinder)} = πr²h}}}}$

Where

• ✮ Radius = r
• ✮ Height = h

$\bold{✍\:According\;To\;Sum}$

$\Large{→\;{\sf{\frac{V_1}{V_2} = \frac{πr²h}{πr²h}}}}$

$\: \: \: \: \: \:$

$\Large{→\;{\sf{\frac{25}{36} = \frac{\cancel{π}r²\cancel{h}}{\cancel{π}r²\cancel{h}}}}}$

$\: \: \: \: \: \:$

$→\;{\sf{25r² = 36r²}}$

$\: \: \: \: \: \:$

$→\;{\sf{(5r)² = (6x)²}}$

$\: \: \: \: \: \:$

$\Large{\red{✎\;{\bf{5:6}}}}$

The ratio radii of the cylinders ◕➜ 5:6

Hope It Helps You ✌️