Question

two cylindrical jars contain the same amount of milk if their diameters are in the ratio 3:4 find the ratio of their heights. with solution

Answer 1

hope it helps

pls vote

Answer 2

Answer:

16:9

Step-by-step explanation:

Let the radius of first cylinder be $r_1$

Let the height of the first cylinder be $h_1$

Volume of first sphere = $\pi r^2 h$

                                    = $\pi r_1^2 h_1$  --1

Let the radius of second cylinder be  $r_2$

Let the height of the second cylinder be $h_2$

Volume of second sphere = $\pi r^2 h$

                                    = $\pi r_2^2 h_2$

We are given that diameters are in the ratio 3:4

$\frac{2r_1}{2r_2}=\frac{3}{4}$

$\frac{r_1}{r_2}=\frac{3}{4}$

[texr_1=\frac{3}{4}r_2[/tex]

Substitute the value in the 1

So, Volume of first sphere = $\pi r^2 h$

                                            = $\pi (\frac{3}{4}r_2)^2 h_1$

Now two cylindrical jars contain the same amount of milk

So, their volumes must be same .

so,  $\pi (\frac{3}{4}r_2)^2 h_1=\pi r_2^2 h_2$

$\frac{9}{16}(r_2)^2 h_1=r_2^2 h_2$

$\frac{9}{16} h_1= h_2$

$h_1= \frac{h_2}{\frac{9}{16}}$

$\frac{h_1}{h_2}= \frac{16}{9}$

Thus  the ratio of their heights is 16:9