Question

The ratio the volume of two cylinders of the same height is 9:16, then what is the ratio of their surface areas ?

Answer 1

$\large{\underline{\red{\rm{QuesTion:}}}}$

The ratio the volume of two cylinders of the same height is 9:16, then what is the ratio of their surface areas.

$\bold\green{\underline{\underline{Given:}}}$

The ratio of the volume of two cyclinder of the same height is 9:16

$\bold\green{\underline{\underline{Find=The\: ratio\:of\: their\: surface\:area:}}}$

$\bold\green{\underline{Let:}}$

The height of 1st cyclinder=h¹

The height of 2nd cyclinder=h²

The radius of 1st cyclinder=r¹

The radius of 2nd cyclinder=r²

$\bold\red{\underline{\underline{A.T.Q:}}}$

Using formula of volume of cyclinder

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

Volume of cyclinder 1st=Volume of cyclinder 2nd

⟹π(r¹)²h¹=π(r²)²h²

⟹Here π cancel on both sides

⟹(r¹)²h¹=(r²)²h²

⟹(r¹)²/(r²)²=h²/h¹

⟹(r¹/r²)²=16/9

⟹r¹/r²=√16/9

⟹r¹/r²=4/3

Now , using formula of surface area

$\bold\purple{\boxed{Surface\:area\:of\: cyclinder=2\:\pi\:r\:h}}$

Calculate for 1st surface area of cyclinder

⟼2πrh

⟼2*π*4*9

⟼72π

Calculate for 2nd surface area of cyclinder

⟼2πrh

⟼2*π*3*16

⟼96π

Hence,

The ratio of their surface area

⟼72π/96π

⟼6/8

⟼3/4

⟼3:4

$\large{\underline{\red{\rm{AnswEr-3:4}}}}$

Answer 2

Answer:

3 : 4

Step-by-step explanation:

We have given :

Ratio of volume is 9 : 16 with same height :

$\displaystyle \sf \dfrac{\pi r^2 . h}{\pi R^2 . h} =\frac{9}{16}$

$\displaystyle \sf \dfrac{r^2}{ R^2} =\frac{9}{16}$

$\displaystyle \sf \dfrac{r}{ R} =\frac{3}{4} \ ... (i )$

Now ratio of surface area :

$\displaystyle \sf \longrightarrow \dfrac{2 \pi r h}{2 \pi R h}$

$\displaystyle \sf \longrightarrow \dfrac{r }{R}$

Using ( i ) we get :

$\displaystyle \sf \longrightarrow \frac{3}{4}$

Therefore , ratio of their surface areas is 3 : 4