A spherical retort 15cm in diameter is half full of acid.The acid is poured into a tall cylindrical breaker of diameter 6cm.How deep is the acid in the beaker
(6/2)^2 * h = 2/3 (15/2)^3
h = 125/4
Ah, the acid's daring escape from the spherical retort! Let's see how far it can dive into the cylindrical breaker.
First, we need to find the volume of the spherical retort. The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius. Since the diameter of the retort is 15cm, the radius (r) is half of that, which is 7.5cm.
V = (4/3)π(7.5^3)
V ≈ 1767.15 cm^3
Since the retort is half full, the volume of acid inside it would be half of the calculated volume:
V_acid = 1767.15 cm^3 / 2
V_acid ≈ 883.57 cm^3
Now, let's find out how deep the acid will be in the cylindrical beaker. The formula for the volume of a cylinder is V = πr^2h, where r is the radius, and h is the height or depth.
We know the diameter of the cylindrical beaker is 6cm, so the radius (r) is half of that, which is 3cm. We can substitute the values we have and solve for h:
883.57 = π(3^2)h
h ≈ 31.27 cm
Therefore, the depth of the acid in the beaker would be approximately 31.27 cm.
But remember, this is just a mathematical calculation. In reality, the acid might not fill the beaker to exactly that depth due to various factors like surface tension, a different pouring process, or maybe even magical chemistry!
125/4
To find out how deep the acid is in the beaker, we can use the concept of equal volumes.
The volume of a sphere is given by the formula:
V_sphere = (4/3) * π * r^3
The volume of a cylinder is given by the formula:
V_cylinder = π * r^2 * h
Given that the retort is half full, the volume of the acid in the retort will be half of the volume of the sphere.
1. Find the volume of the retort:
V_retort = (1/2) * V_sphere
Substituting the value for the diameter of the retort (15 cm) into the formula:
V_retort = (1/2) * (4/3) * π * (15/2)^3
2. Find the volume of the acid in the beaker:
Since the volumes of the retort and the beaker are equal, we can equate the volumes:
V_retort = V_cylinder
(1/2) * (4/3) * π * (15/2)^3 = π * (6/2)^2 * h
Now we can solve for h, the height of the acid in the beaker.
Simplifying the equation:
(1/2) * (4/3) * (225/2)^3 = (3/2)^2 * h
225/2 * 225/2 * 225/2 = 9/4 * h
(225/2)^3 = (9/4) * h
h = (225/2)^3 / (9/4)
Calculating:
h ≈ 94.74 cm
Therefore, the depth of the acid in the beaker is approximately 94.74 cm.
To find the depth of the acid in the beaker, we need to use the concept of volume.
First, let's calculate the volume of the spherical retort. The formula for the volume of a sphere is given by V = (4/3)πr³, where V is the volume and r is the radius.
Given that the diameter of the retort is 15 cm, the radius can be calculated by dividing the diameter by 2: r = 15 cm / 2 = 7.5 cm.
Substituting the value of the radius into the volume formula:
V_retort = (4/3)π(7.5 cm)³
V_retort = (4/3)π(421.875 cm³)
V_retort ≈ 1767.145 cm³
Since the retort is half full of acid, the volume of the acid will be half of the total volume of the retort:
V_acid = 1767.145 cm³ / 2 = 883.5725 cm³
Now, let's calculate the depth of the acid in the cylindrical beaker. The formula for the volume of a cylinder is given by V = πr²h, where h is the height or depth.
Given that the diameter of the beaker is 6 cm, the radius can be calculated by dividing the diameter by 2: r = 6 cm / 2 = 3 cm.
Substituting the values of the radius and volume into the volume formula, we can solve for the height:
883.5725 cm³ = π(3 cm)²h
883.5725 cm³ = π(9 cm²)h
h = 883.5725 cm³ / (π*9 cm²)
h ≈ 31.163 cm
Therefore, the depth of the acid in the cylindrical beaker is approximately 31.163 cm.