Question

A rectangular piece of tin of size 30 centimeters by 18centimetre is rolled in two ways once along its length and once along its breath? Find the ratio of volume of two cylenders so formed

Answer 1

when rolled along it's length,
2πr = 30 cm
r = 15π cm
& length = 18 cm
volume = πr^2 × length
= π × (15π)^2 × 18
= 225/π. ×18
= 4050/π. cm^3

when rolled along it's breath,
2πr = 18 cm
r = 18/2π = 9π cm
& length = 30 cm
volume = π(9π)^2 × 30
= (81×30)/π
= 2430/π. cm^3

hence, the ratio volume of both the cylinders
= (4050/π) / (2430/π)
=5/3

I hope this will help you....

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

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

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

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