Question

a rectangular piece of tin of size 30cm multiply 18 cm is rolled into which ones along its length 30 cm and once along its breadth find the ratio of volumes of two cylinders so formed

Answer 1

Solutions :-

Given :
Length of rectangular piece of tin = 30 cm
Breadth = 18 cm

Find the volume of one cylinder which is rolled along its length :-

2πr = 30
=> r = 30/2π = 15/π

Volume of cylinder = πr²h cu. units
= π × (15/π)² × 18 cm³
= (225 × 18)/π cm³
= 4050/π cm³

Find the volume of other cylinder which is rolled along its breadth :-

2πr = 18
=> r = 18/2π = 9/π

Volume of cylinder = πr²h cu. units
= π × (9/π)² × 30 cm³
= (81 × 30)/π cm³
= 2430/π cm³

Now,
Find the ratio of volumes of two cylinders :-

Ratio of volumes of two cylinders = 4050÷π/2430÷π
= 5/3
= 5 : 3

Hence,
The Ratio of volumes of two cylinders = 5 : 3

Answer 2

$\red{\bold{Hello\:Mate}}$

According to the Question

When rolled with it's length,

2πr = 30 cm

r = 15π cm

Length = 18 cm

Volume = πr^2 × length

= π × (15π)^2 × 18

= $\bf\huge\frac{25}{\pi } \times18$

= $\bf\huge\frac{4050}{\pi }$ cm^3

Rolled along with breath,

2πr = 18 cm

r = $\bf\huge\frac{18}{2\pi }$

= 9π cm

Length = 30 cm

volume = π(9π)^2 × 30

= $\bf\huge\frac{80\times30}{\pi }$

= $\bf\huge\frac{2430}{\pi }$ cm^3

Ratio volume of both the cylinders

= $\bf\huge\frac{4050}{\pi } / \frac{2430}{\pi }$

= $\bf\huge\frac{5}{3}$

$\bf\huge\red{\bold{Thanks}}$