Final answer:
To find the total cost of filling a water tank, we must calculate the total volume using the measurements provided, convert this volume to liters, and then multiply by the cost per liter to find the total cost.
Step-by-step explanation:
The question pertains to finding the total cost of filling a water tank, which is in the shape of a cylinder with a hemispherical top. Given that the total height of the tank is 20 m and the base area is 154 m², we can deduce the height of the cylindrical part since the base area will be the same for both shapes. The volume of a cylinder is given by V_cylinder = πr^2h, and the volume of a hemisphere is V_hemisphere = (2/3)πr^3, where r is the radius of the base and h is the height of the cylinder. Given the base area, A = πr^2 = 154 m², we can solve for r. Once we have r, we can calculate the volumes of both shapes and sum them to find the total volume of the tank.
After finding the volume in cubic meters, we will convert it to liters (1 m³ = 1000 L) since the cost is given per liter. Using the rate of 45 paisa per litre, the cost in rupees (1 rupee = 100 paisa) will give us the total cost to fill the tank. This process involves mathematical operations and unit conversion.
The full solution would include calculating the exact volume and then applying the unit conversions and rate to find the correct cost among the given options.