Given that
length of rectangle=15cm,
breadth of rectangle=12cm,
since the rectangle is curved along its length
length of rectangle= height of cylinder=15cm

Problem:
Find the height of a right circular cylinder made from a rectangle of length 15 cm and breadth 12 cm. It is curved along its length.

Solution:
To find the height of the right circular cylinder, we need to understand the relationship between the dimensions of the rectangle and the cylinder.

Step 1: Identify the dimensions of the rectangle:
Given that the rectangle has a length of 15 cm and a breadth of 12 cm.

Step 2: Understand the transformation:
When the rectangle is curved along its length, it forms the lateral surface of a right circular cylinder. The length of the rectangle becomes the circumference of the cylinder's base, and the breadth of the rectangle becomes the height of the cylinder.

Step 3: Calculate the circumference of the cylinder's base:
The circumference of the base is equal to the length of the rectangle, which is 15 cm.

Step 4: Calculate the radius of the cylinder's base:
To find the radius, we use the formula for circumference: circumference = 2πr. Rearranging the formula, we get r = circumference / (2π). Plugging in the values, we have r = 15 cm / (2π) ≈ 2.39 cm.

Step 5: Calculate the height of the cylinder:
The height of the cylinder is equal to the breadth of the rectangle, which is 12 cm.

Step 6: Conclusion:
Therefore, the height of the right circular cylinder is 12 cm.

Summary:
- The height of a right circular cylinder made from a rectangle curved along its length can be found by equating the breadth of the rectangle to the height of the cylinder.
- The length of the rectangle becomes the circumference of the cylinder's base, and the radius can be calculated using the formula r = circumference / (2π).
- In this particular problem, the height of the cylinder is 12 cm.