A cyhndrical hin 8cm in diameter contains water todepth of 4cm tf a cylindrical wooden rea 4cm in diameter and 6cm long is placed in the tio it Hoars eXaclty half submerged , what is the new clepth of water?
To find the new depth of water when the cylindrical wooden rod is placed in the water, we need to consider the displacement of water caused by the rod.
Let's start by finding the volume of water in the cylindrical tin before the rod is placed in it. The tin has a diameter of 8cm, so the radius (r1) can be calculated by dividing the diameter by 2:
r1 = 8cm / 2 = 4cm
The initial depth of water (h1) is given as 4cm.
The volume of the water (V1) can be found using the formula for the volume of a cylinder:
V1 = π * r1^2 * h1
V1 = π * 4cm^2 * 4cm = 64π cm^3
Now, let's consider the displacement of water caused by the wooden rod. The rod has a diameter of 4cm, so the radius (r2) can be calculated by dividing the diameter by 2:
r2 = 4cm / 2 = 2cm
The length of the rod (h2) is given as 6cm.
The volume of the wooden rod (Vrod) can be found using the formula for the volume of a cylinder:
Vrod = π * r2^2 * h2
Vrod = π * 2cm^2 * 6cm = 24π cm^3
Since the wooden rod is exactly half-submerged, it displaces an equal volume of water, which can be subtracted from the initial volume of water.
Therefore, the new volume of water (Vnew) can be calculated as:
Vnew = V1 - Vrod
Vnew = 64π cm^3 - 24π cm^3
Vnew = 40π cm^3
Finally, we need to find the new depth of water (hnew). Rearranging the formula for the volume of a cylinder, we can solve for hnew:
Vnew = π * r1^2 * hnew
hnew = Vnew / (π * r1^2)
hnew = 40π cm^3 / (π * 4cm^2)
hnew = 10 cm
Therefore, the new depth of water is 10 cm.