The diameter of a solid metal sphere is 18cm. If it is dropped in a completely filled cubical water tank with a side of 20 cm, then what quantity of water will be left in the tank? (Assume density of metal of sphere and density of water to be the sam

To find the quantity of water left in the tank, we need to calculate the volume of the sphere and the volume of the tank.

Step 1: Calculate the volume of the sphere. The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere. Since we are given the diameter, we can find the radius by dividing the diameter by 2. Given diameter = 18 cm Radius = 18 cm / 2 = 9 cm

Now, substitute the radius into the volume formula: V = (4/3)π(9 cm)^3 V ≈ 3053.63 cm^3

Step 2: Calculate the volume of the tank. The volume of a cube is given by V = s^3, where s is the length of the side of the cube. Given side length = 20 cm

Substitute the side length into the volume formula: V = (20 cm)^3 V = 8000 cm^3

Step 3: Calculate the volume of water displaced by the sphere. Since the density of the metal sphere and water are assumed to be the same, the volume of water displaced by the sphere will be equal to the volume of the sphere.

Volume of water displaced = 3053.63 cm^3

Step 4: Calculate the quantity of water left in the tank. To find the quantity of water left in the tank, subtract the volume of water displaced by the sphere from the volume of the tank.

Quantity of water left = Volume of tank - Volume of water displaced Quantity of water left = 8000 cm^3 - 3053.63 cm^3 Quantity of water left ≈ 4946.37 cm^3

Therefore, approximately 4946.37 cm^3 of water will be left in the tank.