The radius of base of the cylindrical tank is 21 cm. Level of water stored in the tank is 3 cm below the top of the tank. When a metallic spherical ball is immersed in the tank, 693 cu. cm of water spills out of the tank. Find the radius of the spherical ball.
Answers
Answer:
The radius of base of the cylindrical tank is 21 cm. Level of water stored in the tank is 3 cm below the top of the tank. When a metallic spherical ball is immersed in the tank, 693 cu. cm of water spills out of the tank. The radius of the spherical ball is 10.5 cm
Step-by-step explanation:
When the spherical ball is immersed in water it displaces its own volume.
The cylindrical tank is not full.
The volume remaining for it to be full is = 22/7 × 21² × 3 = 4158 cm³
So, the total volume of water displaced by the spherical ball :
= 4158 + 693 = 4851 cm³
Volume of the spherical ball = 4851 cm³
We need to work out the radius of the spherical ball.
Let's write down the formula of getting the volume of a sphere.
Volume of a sphere = 4/3πr³
Substituting the values in the formula we have:
4851 cm³ = 4/3πr³
πr³ = 4851 cm³× 3/4
πr³ = 3638.25
r³ = 3638.25 × 7/22
r³ = 1157.625
r = ∛1157.625
r = 10.5 cm
The radius of the spherical ball is equal to 10.5 cm