Question

Two circular cylinder of equal volume have their height in the ratio of 1:2 . The ratio of their radiii is ?​

Answer 1

♠️Question:

Two circular cylinder of equal volume have their height in the ratio of 1:2 . The ratio of their radiii is ?

♠️Answer:

Let the radii of two cylinders be r1 and r2.

Heights be h1 and h2.

Volumes be V1 and V2.

Given, V1 = V2

And ratio of height of cylinders= 1:2

Then , h1:h2=1:2

$\large{ \sf{\to h2 = 2 \times h1}}$

Volume of cylinder=

$\large{ \sf{\to V = \pi {r}^{2} h}}$

♠️According to question :

$\large{ \sf{ \implies{ \red{ \cancel{\pi}}{(r1)}^{2} h1 ={ \red{\cancel{ \pi}} {(r2)}^{2} h2}}}} \\ \large{ \sf{ \: we \: have \: h2 = 2 \times h1}} \\ \\ \large{ \sf{ \star{putting \: the \: value \: of \: h2}}} \\ \large{ \sf{ \implies{(r1) {}^{2} \cancel{h1} =(r2) {}^{2} 2 \cancel{h1}}}} \\ \large{ \sf{ \implies{ {r1}^{2} = r2 {}^{2}}.2}} \\ \large{ \sf{ \implies{r1 = \sqrt{2}r2 }}} \\ \large{ \sf{ \implies{ \frac{r1}{r2} = \frac{ \sqrt{2} \cancel{r1} }{ \cancel{r1}} }}}$

So, the ratio of their radius = root 2 :1

♠️So Final Answer...

$\huge{ \boxed{ \bold{ \red{ \sqrt{2}:1}}}}$

Answer 2

Given

Volume two circular cylinders is equal.

Ratio of heights of both cylinders = 1 : 2

To find

Ratio of their radius

Solution

Here, ratio of heights = 1 : 2

⟼ h₁ : h₂ = 1 : 2

⟼ h₁ = 1 & h₂ = 2

We know that,

➥ Volume of cylinder = πr²h

According to Question now :

➾ πr₁²h₁ = πr₂²h₂

• Cancelling π from both sides

➾ r₁²(1) = r₂²(2)

➾ r₁²/r₂² = 2

• Squaring root on both sides :

➾ r₁/r₂ = √2/1

➾ r₁ : r₂ = √2 : 1

Therefore,

Ratio of volumes of two cylinders = √2 : 1