Question

two circular cylinder of equal volume have their height in the ratio 1.2 find the ratio of their radii ​

Answer 1

Given :

• Two circular cylinder of equal volume have their height in the ratio 1:2.

To find :

• The ratio of their radii.

Solution :

Consider,

• Radii of 1st cylinder = $\sf{r_1}$
• Radii of 2nd cylinder = $\sf{r_2}$

The ratio of their height is 1:2.

Consider,

• Height of 1st cylinder = x
• Height of 2nd cylinder = 2x

Formula Used :-

${\boxed{\bold{Volume\: of \: cylinder=\pi\:r^2h}}}$

★ Volume of 1st cylinder = πr²h

→ $\sf{Volume_{\:\:1st\: cylinder}=\pi\times\:r_1\:^2\times\:x}$

★ Volume of 2nd cylinder = πr²h

→ $\sf{Volume_{\:\:2nd\: cylinder}=\pi\times\:r_2\:^2\times\:2x}$

${\underline{\sf{According\: to \:the\: question:-}}}$

• Two cylinders have equal volume.

$\to\sf{\pi\times\:{r_1}^2\times\:x=\pi\times\:{r_2}^2\times\:2x}$

$\to\sf{r_1\:^2=2r_2\:^2}$

$\to\sf{\dfrac{r_1\:^2}{r_2\:^2}=\dfrac{2}{1}}$

$\to\sf{\dfrac{r_1}{r_2}=\dfrac{\sqrt{2}}{1}}$

$\to\sf{r_1\::\:r_2=\sqrt{2}:1}$

Therefore, the ratio of their radii is √2 : 1.

Answer 2

Answer:

✏️√2 :1

Step-by-step explanation:

♻️Given ♻️:

✏️Two circular cylinders of equal volumes have their heights in the ratio 1:2.

♻️To Find :♻️

✏️Find the ratio of their radii.

♻️Solution♻️ :

✍️we know that the volume of a right circular cylinder with radius r and height h is V=πr²h

✍️It is given that the ratio of the heights of two circular cylinders is 1:2 that is h1/H2=1/2

therefore,

$v1 = v2$

$⇒\pi {r}^{2} 1h1 = \pi {r}^{2} 2h2$

$⇒ \frac{ {r}^{2}1 }{ {r}^{2}2 } = \frac{h2}{h1}$

$⇒ {( \frac{r1}{r2} )}^{2} = 2$

$⇒ \frac{r1}{r2 } = \sqrt{2}$

⚕️ The ratio of the radii is √2:1⚕️