A ball of diameter 20 cm fits exactly inside a cylindrical container.
The maximum volume of liquid which can be poured into the cylindrical container when empty is ________ cm3.
[π=3.14]
you know the cylinder also has a diameter of 20 cm.
It also has a height of 20 cm, so the sphere just fits.
v = pi r^2 h = pi (2/2)^2 (20) = 2000pi
To find the maximum volume of liquid that can be poured into the cylindrical container, we need to find the volume of the cylinder.
The formula for the volume of a cylinder is given by V = πr^2h, where V is the volume, r is the radius, and h is the height.
Since the diameter of the ball is 20 cm, the radius of the ball is half of the diameter, which is 20 cm / 2 = 10 cm.
The height of the cylinder is equal to the diameter of the ball, which is 20 cm.
Substituting these values into the formula, we get:
V = 3.14 * 10^2 * 20
= 3.14 * 100 * 20
= 314 * 20
= 6280 cm^3
Therefore, the maximum volume of liquid that can be poured into the cylindrical container is 6280 cm^3.
To find the maximum volume of liquid that can be poured into the cylindrical container when empty, we need to calculate the volume of the cylinder.
The volume of a cylinder can be found using the formula: V = πr^2h, where V is the volume, r is the radius of the base, and h is the height.
We know that the diameter of the ball is 20 cm, so the radius of the ball is half of the diameter, which is 10 cm.
Now, let's consider the cylinder. Since the ball fits exactly inside the cylinder, the diameter of the cylinder should be equal to the diameter of the ball (20 cm). Therefore, the radius of the cylinder is also 10 cm.
Let's assume the height of the cylinder is h cm.
The maximum volume of liquid that can be poured into the cylindrical container is equal to the volume of the cylinder.
So, substituting the values into the formula, we have:
V = πr^2h
V = 3.14 × 10^2 × h
V = 314h
Now, we need to find the value of h.
Since the ball fits exactly inside the cylindrical container, the height of the cylinder should be equal to the diameter of the ball, which is 20 cm.
Therefore, substituting the value of h, we have:
V = 314 × 20
V = 6280 cm^3
Hence, the maximum volume of liquid that can be poured into the cylindrical container when empty is 6280 cm^3.