Final answer:
To find the ratio of volumes of two cylinders formed by rolling a rectangular piece of tin along its length and its breadth, use the formula for the volume of the cylinder V=πr²h. After calculating, we find that the volume ratio is 0.6, or 3:5.
Step-by-step explanation:
When a rectangular piece of tin is rolled to form a cylinder, the two different dimensions (length and breadth) of the tin will serve as different heights for the cylinder when rolled along them. To find the ratio of volumes of two cylinders formed by rolling along the length and breadth, we use the formula for the volume of a cylinder, V = πr²h.
- When rolled along the length (30 cm), the height (h) is 30 cm, and the radius (r) is half of the breadth, which is 9 cm. So, the volume is V = π(9 cm)²(30 cm).
- When rolled along the breadth (18 cm), the height (h) is 18 cm, and the radius (r) is half of the length, which is 15 cm. So, the volume is V = π(15 cm)²(18 cm).
To find the ratio of the volumes, we simply divide one volume by the other. Since π is a common factor in both volumes, it cancels out:
Ratio = (Volume when rolled along length) / (Volume when rolled along breadth)
= (π(9²)(30)) / (π(15²)(18))
= (9² * 30) / (15² * 18)
= (81 * 30) / (225 * 18)
= 2430 / 4050
= 0.6
So, the ratio of the volumes of the two cylinders is 0.6, or 3:5 when expressed as a ratio.