a cylindrical Jar of radius 12 centimetre contains orange juice to a depth of 20 centimetre child drops and orange into the zar and the level of the juice Rises by 6.75 centimetre what is the radius of the orange if it is of the shape of a complete spare also find the surface area of the orange meritnation

To find the radius of the orange, we can use the concept of displacement of water when an object is submerged in it.

Given:
Radius of the cylindrical jar = 12 cm
Depth of orange juice in the jar = 20 cm
Rise in juice level after dropping the orange = 6.75 cm

Step 1: Calculate the initial volume of the juice before dropping the orange.
The volume of a cylinder is given by the formula:
Volume = π * radius^2 * height

Here, height = 20 cm and radius = 12 cm

Volume of the juice = π * (12 cm)^2 * 20 cm = 2880π cm^3

Step 2: Calculate the final volume of the juice after the orange is dropped.
To find the final volume, we need to consider the rise in the juice level. Since the orange is submerged completely, the volume of the orange is equal to the volume of juice displaced by it.

Volume of juice displaced = Rise in juice level * base area of the cylinder

Base area of the cylinder = π * radius^2

Here, rise in juice level = 6.75 cm

Volume of juice displaced = 6.75 cm * π * (12 cm)^2 = 972π cm^3

Final volume of the juice = Initial volume + Volume of juice displaced
Final volume of the juice = 2880π cm^3 + 972π cm^3 = 3852π cm^3

Step 3: Find the volume of the orange.
Since the orange is in the shape of a sphere, its volume can be calculated using the formula:
Volume of a sphere = (4/3) * π * radius^3

Here, we need to find the radius of the orange, so we rearrange the above formula and solve for radius:
radius = (3 * Volume of the orange) / (4 * π)

Here, Volume of the orange = Final volume of the juice = 3852π cm^3

Substituting this value into the formula, we get:
radius = (3 * 3852π cm^3) / (4 * π) = 2898 / 4 ≈ 724.5 cm

Therefore, the radius of the orange is approximately 724.5 cm.

To find the surface area of the orange, we can use the formula:
Surface area of a sphere = 4 * π * radius^2

Substituting the value of the radius (724.5 cm) into the formula, we get:
Surface area of the orange = 4 * π * (724.5 cm)^2 ≈ 6625071.65 cm^2

Therefore, the surface area of the orange is approximately 6625071.65 cm^2.

To find the radius of the orange, we need to use the concept of displacement of liquid in a cylindrical jar.

First, let's calculate the initial volume of the orange juice in the jar:
The jar is cylindrical, so we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
where:
π is a constant approximately equal to 3.14
r is the radius of the jar (given as 12 cm)
h is the initial depth of the juice in the jar (given as 20 cm)

Plugging in the values, we get:
Initial Volume = π * (12 cm)^2 * 20 cm

Now, when the orange is dropped in the jar, the level of the juice rises by 6.75 cm. This increase in volume is equal to the volume of the orange.

Using the same formula, let's determine the increased volume of the juice in the jar:
Increased Volume = π * r_orange^2 * h_orange
where:
r_orange is the radius of the orange (what we want to find)
h_orange is the increase in the juice level after dropping the orange (6.75 cm)

Now, comparing the initial volume with the increased volume, we can set up the equation:
Initial Volume + Increased Volume = Initial Volume
π * (12 cm)^2 * 20 cm + π * r_orange^2 * 6.75 cm = π * (12 cm)^2 * 20 cm

Simplifying the equation, we can cancel out the common terms:
r_orange^2 * 6.75 cm = 0

Dividing both sides by 6.75 cm, we get:
r_orange^2 = 0

It means that the radius of the orange is zero. This doesn't make sense since the orange has a shape and size. It indicates that there might be an error or inconsistency in the given information or calculation.

As for finding the surface area of the orange, we cannot determine it without knowing the radius.

the volume of the orange is

π * 12^2 * 6.75 = 972π cm^3

Now use what you know about the volume of a sphere to get the radius of the orange, and thus its surface area.