Question

If the radii of two cylinders are in the ratio 3 : 4 and their heights are in the ratio 2 : 9, find the ratio of their curved surface areas ? please give answer of this fast please fast​

Answer 1

Given :-

Ratio of the radius of two cylinder $\sf\ \dfrac{r_1}{r_2}= \dfrac{3}{4}$

Ratio of the height of two cylinder $\sf\ \dfrac{h_1}{h_2}= \dfrac{2}{9}$

To Find :-

We have to find the ratio of the curve surface area of the cylinder

Solution:-

$\bigstar{\textsf{\textbf{\ Curve\ surface\ Area\ of\ cylinder=} }\sf \: 2\pi r h}$

$:\implies\sf\ Ratio\ of\ their\ CSA= \dfrac{CSA_1}{CSA_2}\\ \\ \\ :\implies\sf\ Ratio = \dfrac{2\pi r_1 h_1}{2\pi r_2 h_2}\\ \\ \\ :\implies\sf\ Ratio = \cancel{\dfrac{2\pi }{2\pi }}\times \bigg(\dfrac{r_1}{r_2}\bigg)\times \bigg(\dfrac{h_1}{h_2}\bigg)\\ \\ \\ \bullet\sf\ {\small{substitute\ value\ of\ \dfrac{r_1}{r_2}\ and\ \dfrac{h_1}{h_2}}}\\ \\ \\ :\implies\sf\ \ Ratio = \dfrac{3}{4}\times \dfrac{2}{9}\\ \\ \\ :\implies\sf\ Ratio = \cancel{\dfrac{6}{36}}\\ \\ \\ :\implies\sf\ Ratio = \dfrac{1}{6}\\ \\ \\ \bigstar{\underline{\textsf{\textbf{ Ratio\ of\ their\ CSA= 1:6}}}}$

Answer 2

Given :-

• Ratio of radii = 3:4
• Ratio of height = 2:9

To Find :-

Ratio of CSA

Solution :-

At first we all know that

$\sf CSA = 2\pi rh$

Let the radii be 3r and 4r and height be 2h and 9h

$\sf \dfrac{CSA}{CSA'} = \dfrac{2 \times 22/7 \times 3r \times 2h}{2 \times 22/7 \times 4r \times 9h}$

cancel 2

$\sf \dfrac{CSA}{CSA'} = \dfrac{22/7 \times 3r \times 2h}{22/7 \times 4r \times 9h}$

Cancel 22/7

CSA/CSA' = 3r × 2h/4r × 9h

CSA/CSA' = 3 × 2/4 × 9

CSA/CSA' = 6/36

CSA/CSA' = 1/6