1. A pond with a length of 40 meters and a width of 30 meters costs ₹51,000 to dig, at a rate of ₹8.50 per cubic meter. What is the depth of the pond?

(a) 7 meters (b) 12 meters (c) 5 meters (d) 10 meters

2. 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]

3. A roof measuring 13 meters in length and 11 meters in width had its drainage pipe closed during rainfall. After the rain, it was found that water had accumulated to a depth of 7 centimeters on the roof. The pipe through which the water drains has a diameter of 7 centimeters and discharges water in the form of a cylindrical stream at a rate of 200 meters in length per minute. Determine how long it will take for all the water to drain out once the pipe is opened.

4. A pump can fill 37,400 liters of water per hour. Then, how long should the pump be operated to fill an amount of water up to a height of 17 decimeters in a rectangular tank that is 18 meters long and 11 meters wide?

5. A wooden box with a 5 cm thick lid is made from wooden planks. Its weight is 115.5 kg, and when filled with rice, it weighs 880.5 kg. The internal length and breadth of the box are 12 decimeters and 8.5 decimeters respectively, and the weight of rice per cubic decimeter is 1.5 kg. **(1) Calculate and write the internal height of the box.** **(2) At a rate of ₹1.50 per square decimeter, calculate the total cost to paint the outer surface of the box (excluding the base).**

6. The base length and width of a rectangular reservoir are 15 meters and 12 meters respectively. Water is filled into the reservoir from a nearby pond using a pump. If the pump can fill 36,000 liters of water per hour, then how long will it take for the pump to fill the reservoir up to a height of 7.2 decimeters? [Note: 1 liter = 1 cubic decimeter]

7. A hollow cylindrical iron pipe is 6 meters long. Its internal and external diameters are 3.5 cm and 4.2 cm respectively. Calculate the volume of iron in the pipe. If the weight of iron is 5 kg per cubic decimeter, then find the total weight of the pipe.

8. In our Bakultala village, a canal has been dug that is 2 meters wide and 8 decimeters deep. If a total of 240 cubic meters of soil has been excavated, calculate and write the length of the canal.

9. A rectangular water tank is 2.1 meters long and 1.5 meters wide, and is currently half full of water. If 630 liters of water are added to the tank, calculate and write how much the water level (depth) will rise.

10. The diameter of a right circular cone is 21 meters and its height is 14 meters. Calculate how much it will cost to paint the lateral surface of the cone at a rate of 1.50 rupees per square meter.

11. The base diameter of a solid cone-shaped wooden toy is 10 cm. The curved surface of the toy is polished at the rate of ₹2.10 per square centimeter, with a total cost of ₹429. Calculate the height of the toy. Determine how many cubic centimeters of wood were used to make the toy.

12. For digging a well of depth \(x\) decimeters, one part of the total cost varies directly with \(x\), and the other part varies directly with \(x^2\). If the cost of digging 100 decimeters and 200 decimeters deep wells is ₹5000 and ₹12000 respectively, then calculate the cost of digging a 250 decimeter deep well.