3. Find the missing dimension for a cylinder. (Take \( \pi=\frac{22}{7} \) (fi) Radius; Curved surface area \( =220 \mathrm{~cm}^{2} \), Height \( =10 \mathrm{~cm} \)

To find the missing dimension, which is the radius, you can use the formula for the curved surface area of a cylinder: \( \text{Curved Surface Area} = 2\pi rh \). Given that the curved surface area is \( 220 \, \text{cm}^2 \) and the height \( h = 10 \, \text{cm} \), the equation becomes: \[ 220 = 2 \times \frac{22}{7} \times r \times 10 \] Now, rearranging for \( r \): \[ r = \frac{220 \times 7}{2 \times 22 \times 10} \] \[ r = \frac{220 \times 7}{440} = \frac{1540}{440} = 3.5 \, \text{cm} \] So the missing dimension, the radius, is \( 3.5 \, \text{cm} \). Did you know that the first known usage of cylinders dates back to ancient Mesopotamia, where they were used as seals to mark property and ownership? The simple yet effective design has withstood the test of time, making cylinders a fundamental shape in mathematics and engineering! In practical scenarios, understanding the curvature and dimensions of cylinders can be hugely beneficial. For example, in manufacturing, knowing the proper dimensions helps in designing cans, pipes, or any cylindrical containers, ensuring that they hold the correct volume and withstand pressure efficiently! Remember: always double-check your calculations to avoid mix-ups in dimensions!