Question

Two circular cylinders of equal curved surface
have their heights in the ratio 1:2. Find the ratio of their radii.

Answer 1

Correct Question :

♦ Two circular cylinders of equal curved surafe areas have their heights in the ratio 1 : 2. Find the ratio of their radii.

$\bf {\huge {\underline {\boxed {\sf\pink {Answer :- \:1 : 2 }}}}}$

$\textbf {\underline {\underline {Step-By-Step\:Explanation:}}}$

$\textbf {\blue{\underline {Given:}}}$

• Two circular cylinders have equal curved surface area.
• Their heights are in the ratio 1 : 2

$\textbf {\pink {\underline {To\:Find:}}}$

• Ratio of their radii

$\huge\underline\green{\tt Solution:}$

Let the height of first cylinder be ' $h_1$ ' and the second cylinder's height be ' $h_2$'. Similarly for radius, Radius of first cylinder be $r_1$ and for second be $r_2$.

It is given that,

C.S.A of first cylinder = C.S.A of second cylinder. -------------( 1 )

Also,

$\dfrac {h_ 1}{h_ 2}$ = $\dfrac {1}{2}$

Now,

$2\pi {r_1}{h_1} = 2\pi {r_2}{h_2}$

➡ $\cancel {2\pi}{r_1}{h_1} = \cancel {2\pi}{r_2}{h_2}$

➡ $\dfrac {r_1}{r_2} = \dfrac {h_1}{h_2}= \dfrac {2}{1}$

•°• $\dfrac {r_1}{r_2} = \dfrac {1}{2}$

Hence,

Answer : The ratio of their radii is 2 : 1

Answer 2

Answer:

The ratio of their radii is 1 : 2.

Step-by-step explanation:

To Find :

The ratio of their radii.

Solution :

As given,

• Two circular cylinders of equal curved surface
• They have their heights in the ratio 1:2.
• C.S.A of first cylinder = C.S.A of second cylinder.

We know that :

$\bigstar\;\boxed{\textsf{The volume of cylinder}= \bf \pi r^2\;h}}$

Now,

Consider the :

The radius of cylinder as -  r₁ and r₂

The height of first cylinder as -  h₁

The second cylinder's height as - h₂

As given,

C.S.A of first cylinder = C.S.A of second cylinder.

____________[Equation 1]

Now,

$\sf \implies \dfrac {h_ 1}{h_ 2} = \dfrac {1}{2}$

So,

$\sf\\ \\\implies 2\pi {r_1}{h_1} = 2\pi {r_2}{h_2}\\ \\ \\ \implies {2\pi}{r_1}{h_1} = {2\pi}{r_2}{h_2}\\ \\ \\ \implies \dfrac{r_1}{r_2} = \dfrac{h_1}{h_2}= \dfrac{2}{1}\\ \\ \\\implies \dfrac{r_1}{r_2} = \dfrac {1}{2}$

∴ The ratio of their radii is 1 : 2.