Question

The diameters of two cylinders having same height are in the ratio 2:3

a) What is the ratio of their radii ?

b) What is the ratio of their volumes?​

Answer 1

Answer:

Given : diameters of two cylinders having the same height = 2 : 3 Read more on Sarthaks.com - https://www.sarthaks.com/209596/the-diameters-of-two-cylinders-having-the-same-height-are-in-the-ratio-2-3

Answer 2

$\\ \large \underline \bold{ \: Given :- }$

★ The diameters of two cylinders having same height are in the ratio 2:3.

$\\ \large \underline \bold{ \: To \: find :- }$

• a) What is the ratio of their radii ?

• b) What is the ratio of their volumes?

$\\ \large \underline \bold{ \: Solution :- }$

$\\ \rm{a)} \sf \: The \: diameters \: of \: two \: cylinders \: \\ \sf having \: same \: height \: are \: in \: the \: ratio \: 2:3.$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{D_1}{D_2} = \frac{2}{3}$

$\\ \\ \sf \: \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: : \implies \: \frac{2r_1}{2r_2} = \frac{2}{3}$

$\\ \\ \sf \: \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: : \implies \: \bigg(\frac{r_1}{r_2} \bigg) = \frac{2}{3}$

$\\ \: \: \: \: \: \: \: \: \sf \underline{ \boxed{ \: \sf \: \therefore \: Ratio \: of \: their \: radii \: = \: \frac{2}{3} \: \: \: \: \: }}$

b) Ratio of volume of cylinder

→ πr²_1 h / πr²_2 h

→( r1 / r2)² = (2/3)² = 4/9

Ratio of volume of cylinder is 4/9 .