Answer:
To find the cost of filling Binaya's water tank, we need to calculate the volume of the tank first. The tank is in the shape of a cylinder surmounted by a hemisphere, so we can find the volume by calculating the volumes of the cylinder and hemisphere separately and adding them together.
The formula for the volume of a cylinder is V_cyl = πr^2h, where r is the radius and h is the height.
Given that the internal radius of the tank is 90 cm and the total height is 3.8 m, we convert the height to cm to match the radius unit and get 380 cm in height.
So, the volume of the cylinder part of the tank will be V_cyl = π(90)^2(380) = 9147600 cm^3.
The formula for the volume of a hemisphere is V_hem = (2/3)πr^3, where r is the radius of the hemisphere. By halving the internal radius of the cylinder, we get the radius of the hemisphere as 45 cm.
So, the volume of the hemisphere part of the tank will be V_hem = (2/3)π(45)^3 = 95325π cm^3.
The total volume of the tank will be the sum of the volumes of the cylinder and hemisphere:
V_total = V_cyl + V_hem = 9147600 + 95325π = 9457589.25 cm^3.
To convert this volume to litres, we divide by 1000:
V_total_l = 9457.59 l.
The cost of filling the tank with water at the rate of 20 paisa per litre will be:
Cost = 9457.59 x 0.20 = 1891.52 paisa = 18.92 rupees (rounded to two decimal places).
Therefore, it will cost Binaya 18.92 rupees to fill his water tank with water at the given rate.