Question

Is it possible to calculate the volume of a sample black cylinder using a water displacement apparatus? The inside diameter of the glass is 2.857 cm and the scale on its surface is graduated in cm. The inside diameter of the metal beaker is 7.745 cm. (We had one glass and one metal cylinder. We droped objects in the metal cylinder and noted the initial volume of the water and the final volume of the water.)

Answer 1

Yes it is possible to measure the volume of an object if we know the volume of water it displaced when dipped in a cylinder filled with water.

Here we know radius of the cylinder is 7.745 cm,

Thus the area of the base of the cylinder is (3.14 x 7.745^2) cm^2

Let's the intial height of the water level in cylinder is h1 cm

And final height of the water level after dipping the object (of which we want to know the volume) is h2 cm.

Then the height of the water level raised by dipping the object is (h2 - h1) cm.

So the volume of the object dipped in the water

= volume of the water displaced by it after dipping in water

= (base area of the cylinder) x (height raised of water level after dipping of the object in water.) = 3.14 x 7.745^2 x (h2-h1) cm^3.