Question

Plzzz ans it guys


The radii of two right circular cylinder are in the ratio 1:3 and the ratio of csa is 5:6 Find the ratio of their height​

Answer 1

Gɪᴠᴇɴ :-

• The radii of two right circular cylinder are in the ratio = 1:3
• Ratio of Their CSA = 5:6

Tᴏ Fɪɴᴅ :-

• Ratio of Their Heights ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• CSA of cylinder = 2 * π * r * h

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume that heights of both cylinders is h1 & h2.

Also Assume That, their radius is x & 3x and, their CSA is 5y & 6y .

Than, we can conclude That ,

→ 2 * π * x * h1 : 2 * π * 3x * h2 = 5y : 6y

→ (2 * π * h1 * x) / (2 * π * 3x * h2) = (5y/6y)

→ (h1 * 1) / (3 * h2) = (5/6)

→ h1/h2 = (5 * 3) / (6*1)

→ h1/h2 = (5 / 2)

→ h1 : h2 = 5 : 2 (Ans.)

Hence, Ratio of Their Heights will be 5:2 .

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

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

• Radii of C.SA = 1:3
• Ratio of C.S.A = 5:6

${\bf{\blue{\underline{To\: Find:}}}}$

• Ratio of their height

${\bf{\blue{\underline{Now:}}}}$

• Let Radii of first cylinder= 1x
• And Radii of second cylinder = 3x
• Let first ratio of CSA = 5y
• And second Ratio = 6y

$\bigstar\boxed{\bf{\green{\underline{ \: curved \: surface \: area \: of \: cylinder = 2\pi \: rh}}}}$

$: \implies{\sf{ ratio \: of \: their \: surface \: area = \frac{5}{6} }}$

$: \implies{\sf{ \frac{2\pi \: rh}{2\pi \: RH} = \frac{5}{6} }}$

$: \implies{\sf{ \frac{\: rh}{ \: RH} = \frac{5y}{6y} }}$

$: \implies{\sf{ \frac{\: (1x)h}{ \: (3x)H} = \frac{5y}{6y} }}$

$: \implies{\sf{ \frac{\: 1xh}{ \: 3xH} = \frac{5y}{6y} }}$

$: \implies{\sf{ \frac{\: h}{ \: H} = \frac{5 \times 3}{6 \times 1} }}$

$: \implies{\sf{ \frac{\: h}{ \: H} = \frac{15}{6 } }}$

$: \implies{\sf{ \frac{\: h}{ \: H} = \frac{5}{2 } }}$

Hence the Ratio of their height is h:H =5:2.