Question

দুটি লম্ব বৃত্তাকার চোঙের উচ্চতার অনুপাত 1 : 2 এবং ভুমির পরিধির অনুপাত 3 : 4 হলে, তাদের আয়তনের
অনুপাত নির্ণয় করাে।​

Answer 1

The ratio of height of two perpendicular round tubes is 1: 2 and the ratio of circumference of land is 3: 4, their volume.  Determining the ratio.

Given that,

The ratio of height of two perpendicular round tubes is 1:2.

The ratio of circumference of land is 3:4

To find,

The ratio of the volume of the tubes.

Solution,

Circumference is given by :

$C=2\pi r$

The ratio of two round tubes,

$\dfrac{C_1}{C_2}=\dfrac{r_1}{r_2}=\dfrac{3}{4}$

When two round tubes are joined, it will form cylinder. The volume of a cylinder is given by :

$V=\pi r^2 h$

So,

$\dfrac{V_1}{V_2}=\dfrac{r_1^2h_1}{r_2^2 h_2}\\\\\dfrac{V_1}{V_2}=(\dfrac{3}{4})^2\times \dfrac{1}{2}\\\\\dfrac{V_1}{V_2}= \dfrac{9}{32}$

So, the ratio of the volumes of the round tubes is 9:32.