1. A rectangular playground is 45 meters long and 40 meters wide. There is a road of uniform width built around the playground. The area of the road is 450 square meters. — Form a quadratic equation with one variable from the given statement.

2. A rectangular piece of soft cardboard has a length that is four times its width. When rolled along its length, it forms a right circular cone whose lateral surface area is 100 square centimeters. What is the height of the cone?

3. The rectangular village field has a length of 20 meters and a width of 15 meters. To install pillars at the four corners, four cube-shaped holes of 4 meters in length were dug and the removed soil was spread evenly over the remaining area of the field. Calculate how much the surface level of the field will rise.

4. A rectangular pond is 20 meters long and 18.5 meters wide, and contains water to a depth of 3.2 meters. A pump that can irrigate 160 kiloliters of water per hour is used to remove all the water from the pond. Calculate and write how long it will take to pump out all the water. If this water is then used to irrigate a field with embankments measuring 59.2 meters in length and 40 meters in width, calculate and write the depth of water that would cover the field. [Note: 1 cubic meter = 1 kiloliter]

5. In our neighborhood, there are two houses on opposite sides of the road facing each other. If the base of a ladder is placed 6 meters away from the foot of the wall of the first house and the ladder is leaned against the wall, it makes an angle of 30° with the horizontal. But if the same ladder is placed in the same position and leaned against the wall of the second house, it makes an angle of 60° with the horizontal. (i) Find the length of the ladder. (ii) Calculate how far the foot of the ladder is from the base of the second house. (iii) Find the width of the road. (iv) Determine the height at which the top of the ladder touches the second house.