A spherical container 15cm in diameter is half full of acid.the acid is poured into a tall cylindrical beaker of diameter 6cm how deep is the acid in the beaker

v = 1/2 (4/3 * pi * (15/2)^3) = 1125/4 pi

So, in a beaker of cross-section pi*(6/2)^2 = 9 pi,

depth is (1125/4 pi) / (9 pi) = 31.25 cm

Well, well, well, acid seems to be making quite the splash here! Now, if we have a spherical container that's half-full of acid, we can imagine it as a hemisphere. The diameter of the hemispherical acid is 15 cm, so its radius would be half of that, which is 7.5 cm.

Now, this wild acid party wants to move into a cylindrical beaker with a diameter of 6 cm. The height of the acid in the beaker would determine how deep it is.

Since the beaker has a smaller diameter than the hemisphere, the acid will occupy less space. So, let's break out some math magic. We know that the volume of a hemisphere is (2/3)πr³, and the volume of a cylinder is πr²h, where r is the radius and h is the height.

Since the acid-filled hemisphere has a radius of 7.5 cm, its volume would be (2/3) * π * (7.5)^3.

Now, the volume of the acid in the cylindrical beaker would be π * (3^2) * h, since the radius of the beaker is 3 cm and we're solving for the height, h.

Since the acid is transferred from the hemisphere to the beaker, their volumes must be the same. Therefore, we can set up the equation:

(2/3) * π * (7.5^3) = π * (3^2) * h

Now, let's cancel out some π and solve for h:

(2/3) * (7.5^3) = (3^2) * h

(2/3) * (7.5^3) = 9 * h

h = (2/3) * (7.5^3) / 9

After a bit of calculation, my friend, you'll find that the depth of the acid in the beaker would be about 6.25 cm.

So, we have acid hanging out around 6.25 cm deep in the beaker. Watch out for any wild acid parties that might break out!

To find the depth of the acid in the beaker, we need to compare the volumes of the spherical container and the cylindrical beaker.

Let's start by calculating the volume of the spherical container.

The formula for the volume of a sphere is:
V_sphere = (4/3) * π * r^3

Given that the diameter of the spherical container is 15 cm, the radius (r) can be calculated as half of the diameter:
r = 15 cm / 2 = 7.5 cm

Substituting the radius value into the volume formula, we get:
V_sphere = (4/3) * π * (7.5 cm)^3

Now let's calculate the volume of the cylindrical beaker.

The formula for the volume of a cylinder is:
V_cylinder = π * r^2 * h

Given that the diameter of the cylindrical beaker is 6 cm, the radius (r) can be calculated as half of the diameter:
r = 6 cm / 2 = 3 cm

We need to find the height (h) of the acid in the beaker.

Since we know that the spherical container is half full, the volume of the acid in the beaker should be equal to half of the volume of the spherical container.

Therefore, we can set up the equation:
V_cylinder = (1/2) * V_sphere

π * (3 cm)^2 * h = (1/2) * [(4/3) * π * (7.5 cm)^3]

Simplifying further, we have:
9π * h = (1/2) * (4/3) * 7.5^3 * π

Cancelling out common terms and solving for h, we get:
h = [(1/2) * (4/3) * 7.5^3] / 9

Evaluating this expression, we find:
h ≈ 5 cm

Therefore, the depth of the acid in the beaker is approximately 5 cm.

To find the depth of the acid in the beaker, we need to first calculate the volume of the acid and then divide it by the cross-sectional area of the beaker.

Let's start by finding the volume of the acid in the spherical container. The formula for the volume of a sphere is given as V = (4/3)πr^3, where V is the volume and r is the radius.

Given that the diameter of the spherical container is 15 cm, the radius (r) can be calculated as half of the diameter, which is 15/2 = 7.5 cm.

Plugging this value into the volume formula:

V = (4/3) * π * (7.5)^3
≈ 1767.15 cm^3

Now, since the spherical container is half full, the volume of the acid is half of the calculated volume:

V_acid = 1767.15 cm^3 / 2
= 883.58 cm^3

Next, we need to calculate the cross-sectional area of the beaker. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.

Given that the diameter of the beaker is 6 cm, the radius (r) can be calculated as half of the diameter, which is 6/2 = 3 cm.

Plugging this value into the area formula:

A = π * (3)^2
= 28.27 cm^2

Finally, we can determine the depth of the acid in the beaker by dividing the volume of the acid by the cross-sectional area of the beaker:

Depth = V_acid / A
= 883.58 cm^3 / 28.27 cm^2
≈ 31.25 cm

Therefore, the depth of the acid in the beaker is approximately 31.25 cm.