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 . What is the volume of the rock?
To solve this problem, we need to calculate the increase in the volume of water in the tank when the rock is thrown in. We can then use this increase in volume to find the volume of the rock.
Given:
- Diameter of the cylindrical water tank = 1.5m
- Increase in water level after the rock is thrown in = 1.5cm = 0.015m
First, we need to calculate the increase in the volume of water in the tank:
Volume of water in the tank = πr^2h, where r is the radius of the tank and h is the height of water before the rock is thrown in.
Since the diameter of the tank is 1.5m, the radius (r) = 1.5/2 = 0.75m
Initial volume of water in the tank = π(0.75)^2h = π(0.5625)h
After the rock is thrown in, the volume of water in the tank will be:
Volume of water in the tank after rock is thrown in = π(0.75)^2( h + 0.015) = π(0.5625)(h + 0.015)
Increase in volume of water in the tank = π(0.5625)(h + 0.015) - π(0.5625)h
= π(0.5625)(h + 0.015 - h)
= π(0.5625)(0.015)
≈ 0.0265 cubic meters
Since the increase in volume of water is equal to the volume of the rock, the volume of the rock is approximately 0.0265 cubic meters.