To estimate the volume of a large rock , the rock is thrown into a cylindrical water tank of diameter 1.5m which is nearly full of water .it's is noted that the water level in the tank rises by 1.5cm . If the rock is roughly spherical, what is its diameter?
To estimate the volume of the rock, we can use the principle of displacement, where the volume of water displaced by the rock is equal to the volume of the rock itself.
Since the water level in the tank rises by 1.5cm when the rock is thrown in, this is the amount of water that has been displaced by the rock.
First, let's calculate the volume of water displaced:
Volume of water displaced = area of the base of the cylindrical tank * change in height of the water level
Volume of water displaced = π(0.75)^2 * 0.015
Volume of water displaced = π(0.5625) * 0.015
Volume of water displaced = 0.02526 m^3
Since the volume of water displaced by the rock is equal to the volume of the rock itself, we can use the volume formula for a sphere to find its diameter:
Volume of sphere = (4/3)πr^3
0.02526 = (4/3)π(r^3)
0.02526 * 3/4π = r^3
r^3 = 0.031575
Taking the cube root of both sides to solve for r:
r = 0.3485 m
Therefore, the diameter of the rock is twice the radius:
Diameter = 2 * 0.3485 = 0.697 m
So, the estimated diameter of the rock is approximately 0.697 meters.