Q4. The circumference of a right circular cylinder is 440 cm and its height is 5 cm. Find the lateral surface area of the cylinder.

To find the lateral surface area of the cylinder, we use the formula \( LSA = 2\pi rh \), where \( r \) is the radius, and \( h \) is the height. First, we find the radius from the circumference formula \( C = 2\pi r \). Given \( C = 440 \) cm, we rearrange it to find \( r \): \[ r = \frac{C}{2\pi} = \frac{440}{2\pi} = \frac{220}{\pi} \approx 70.4 \text{ cm}. \] Now, we can calculate the lateral surface area: \[ LSA = 2\pi rh = 2\pi \left(\frac{220}{\pi}\right)(5) = 2200 \text{ cm}^2. \] So, the lateral surface area of the cylinder is \( 2200 \) cm². Now, let's add some extra information! Long ago, ancient cultures like the Egyptians utilized cylinder shapes in their architecture and art, symbolizing stability and eternity. The cylindrical forms are not just for storage or vessels; they can also be seen in famous structures like the Colosseum, illustrating the importance of geometry throughout history! In practical terms, the lateral surface area of a cylinder is crucial for various applications, such as when painting or wrapping cylindrical objects. If you're putting on a coat of paint, for instance, knowing this area helps ensure you're not short on supplies! Just remember that measuring twice is better than running back to the store!