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.
​

Answer 1

Answer:

SOLUTION:

Let the Diameter of the container 1 be D₁.

Let the Diameter of container 2 be D₂.

Then, we can easily write that:

$\frac{D_1}{D_2} =\frac{3}{4}$

Substitute D₁=2πr₁.

D₂=2πr₂.

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

Cancel out 2π.

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

Now, since they have the same amount of milk, their volumes are same.

Thus, $Volume_1=Volume_2$

Transpose Volume₂ to LHS.

$\frac{Volume_1}{Volume_2} =1$

We can substitute Volume₁=πr²₁h₁ and Volume₂=πr²₂h₂.

$\frac{\pi r_1^2 h_1}{\pi r_2^2h_2} =1$

Cancel out π.

$\frac{ r_1^2 h_1}{ r_2^2h_2} =1$

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

$\frac{ 3^2 h_1}{4^2h_2} =1$

$\frac{9 \times h_1}{16 \times h_2} =1$

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

Thus, the Ratio of height of the smaller container and bigger container is 16:9 and the Ratio of height of the bigger container and smaller container is 9:16.

HOPE THIS HELPS :D