Question

a rectangular piece of tin of size 30 cm X 18 cm is rolled into two ways 1 along its length and 1 along its breadth find the ratio of the volumes of two cylinders so formed.

Answer 1

ratio of volume of cylinder1:volume of cylinder2
=773.18/1288.63
=77318:128863

Answer 2

Answer:

The ratio of the volumes of the cylinders is 5 : 3.

Step-by-step explanation:

We are given the dimensions of the rectangle are,

Length = 30 cm

Width = 18 cm

We know that, Volume of a cylinder = $\pi r^{2}h$

Way 1: The rectangle is rolled along the length.

Then, the dimensions of the cylinder formed are,

Height = 18 cm

Circumference = 30 cm i.e. $2\pi r=30$ i.e. $r=\frac{15}{\pi }$

Then, Volume of the 1st cylinder, $V_{1}=\pi (\frac{15}{\pi})^{2}\times 18$

i.e. Volume of the 1st cylinder, $V_{1}=\frac{4050}{\pi}$

i.e. Volume of the 1st cylinder, $V_{1}=1289.16$ cm³

Way 2: The rectangle is rolled along the width.

Then, the dimensions of the cylinder formed are,

Height = 30 cm

Circumference = 18 cm i.e. $2\pi r=18$ i.e. $r=\frac{9}{\pi }$

Then, Volume of the 2nd cylinder, $V_{2}=\pi (\frac{9}{\pi})^{2}\times 30$

i.e. Volume of the 2nd cylinder, $V_{2}=\frac{2430}{\pi}$

i.e. Volume of the 2nd cylinder, $V_{2}=773.49$ cm³.

Thus, the ratio of the volume of the cylinders is,

$\frac{V_1}{V_2}=\frac{1289.16}{773.49}=\frac{5}{3}$[/tex] cm³

Hence, the ratio of the volumes of the cylinders is 5 : 3.