Question

The height of two cylinders are in the ratio 7: 9 and their curved surface areas are in the ratio 7:6, then the ratio of their volumes is​

Answer 1

Answer:

Ok

Step-by-step explanation:

Conduction is the transfer of thermal energy through direct contact. Convection is the transfer of thermal energy through the movement of a liquid or gas.

Answer 2

Given data:

The height of two cylinders are in the ratio $7:9$ and their curved surface areas are in the ratio $7:6$

To find:

The ratio of their volume

Step-by-step explanation:

Step 1.

Let $h_{1},h_{2}$ be their heights

$\Rightarrow h_{1}:h_{2}=7:9$

$\Rightarrow \dfrac{h_{1}}{h_{2}}=\dfrac{7}{9}$ ... ... (i)

Step 2.

Let $A_{1},A_{2}$ be their curved surface areas

$\Rightarrow A_{1}:A_{2}=7:6$

$\Rightarrow \dfrac{A_{1}}{A_{2}}=\dfrac{7}{6}$ ... ... (ii)

Step 3.

Let $r_{1},r_{2}$ be the radii of their bases

Then from (ii), we get

$\quad\dfrac{2\pi r_{1}h_{1}}{2\pi r_{2}h_{2}}=\dfrac{7}{6}$

$\Rightarrow \dfrac{r_{1}}{r_{2}}\times \dfrac{h_{1}}{h_{2}}=\dfrac{7}{6}$

$\Rightarrow \dfrac{r_{1}}{r_{2}}\times \dfrac{7}{9}=\dfrac{7}{6}$, [by (i)]

$\Rightarrow \dfrac{r_{1}}{r_{2}}=\dfrac{3}{2}$ ... ... (iii)

Step 4.

If $V_{1},V_{2}$ be their volumes, then

$\quad\dfrac{V_{1}}{V_{2}}$

$=\dfrac{\pi {r_{1}}^{2} h_{1}}{\pi {r_{2}}^{2} h_{2}}$

$=(\dfrac{r_{1}}{r_{2}})^{2}\times\dfrac{h_{1}}{h_{2}}$

$=(\dfrac{3}{2})^{2}\times\dfrac{7}{9}$, [ by (i) and (iii) ]

$=\dfrac{9}{4}\times\dfrac{7}{9}$

$=\dfrac{7}{4}$

$\Rightarrow V_{1}:V_{2}=7:4$

Final answer:

The ratio of their volumes is $7:4$.