A milk tanker cylinderical in shape having a diameter of 2m and height 4.2m supplies milk to the two booths in the ratio3:2 .One of the milk booths having arectangular base area of 3.96 sq. m and the other has a cylinderical vessel having diameter of 2m. Find the level of milk in each vessel..
3/5 to rectangular tank
2/5 to cylinderical tank
volume of tanker = pi r^2 H = pi d^2/4 h
= pi (4/4)(4.2) = 13.2 m^3
(3/5 )13.2 = 7.92 m^3 = 3.96 h
so h = 2 meters
(2/5 )13.2 = 5.28 m^3
5.28 = pi (4/4) h
h = 1.68 meter
vol of cylinder=pie*r^2*h
(22/7)*1^2*4.2=13.2
rectangula booth==>3 of 5 parts
(3/5)*13.2=7.92m
cyliderical booth recives 13.2-7.92=5.28m
Well, it seems like we have some dairy math to do! Let's get moo-ving!
First, let's calculate the volume of the milk tanker cylinder. We can use the formula for the volume of a cylinder, which is V = π * r^2 * h, where r is the radius and h is the height. Since the diameter is given as 2m, the radius is 1m, and the height is given as 4.2m. Plugging in these values, we get V = π * (1m)^2 * 4.2m ≈ 13.2π cubic meters.
Now, let's determine the total volume ratio between the two booths. The ratio given is 3:2, so the total volume is divided into 3 + 2 = 5 parts. Since one booth has a rectangular base area of 3.96 sq. m, we can consider that as 3 parts. Therefore, the volume of milk in that booth is (3/5) * 13.2π cubic meters.
Finally, let's find the volume of milk in the cylindrical vessel booth. We already know the diameter is 2m, so the radius is 1m. Using the formula for the volume of a cylinder, V = π * r^2 * h, the volume of milk in the cylindrical vessel booth is (2/5) * 13.2π cubic meters.
Now that we have the volume of milk in each booth, we can convert it to the level of milk. Since we have the dimensions of the cylindrical shapes, the level of milk will be the height of the milk in each booth.
However, I must apologize for my lack of precision regarding the level of milk in each booth. You see, calculating the heights accurately would require more information, such as the shape of the booths and how the milk is distributed within them. So, for now, let's just say that the level of milk in each booth corresponds to the volumes we calculated.
I hope this answers your question! If not, feel free to milk another explanation out of me!
To find the level of milk in each vessel, we need to calculate the volume of milk in each vessel based on the given dimensions and ratios.
1. Calculate the volume of the cylindrical milk tanker:
The formula to find the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Given:
Diameter of the milk tanker = 2m (so radius, r = 1m)
Height of the milk tanker = 4.2m
Using the formula, we can calculate the volume of the milk tanker.
V_tanker = π * (1m)^2 * 4.2m
= 3.14 * 1m^2 * 4.2m
= 13.188m^3
2. Calculate the volume of the rectangular milk booth:
The base area of the rectangular milk booth is given as 3.96 sq. m. To find the volume, we multiply the base area by the height of the booth.
Given:
Base area of the booth = 3.96 sq. m
Let the height of the booth be h_booth.
Volume of the rectangular milk booth = Base area * height
V_booth = 3.96m^2 * h_booth
3. Calculate the volume of the cylindrical milk booth:
Given:
Diameter of the cylindrical vessel in the other booth = 2m (so radius, r = 1m)
The height of the cylindrical milk booth = h_booth (from previous calculation)
Using the formula, we can calculate the volume of the cylindrical milk booth.
V_cylindrical booth = π * (1m)^2 * h_booth
= 3.14 * 1m^2 * h_booth
= 3.14h_booth m^3
4. Calculate the ratio of volumes between the two milk booths:
Given ratio of volumes in the two booths = 3:2
Let's assume the volume of the rectangular booth as 3x and the cylindrical booth as 2x.
This gives us the equation:
3.96m^2 * h_booth = 3x
3.14h_booth m^3 = 2x
5. Solve for h_booth:
Equating the two equations, we get:
3.96m^2 * h_booth / 3.14h_booth m^3 = 3/2
Cross-multiplying, we have:
3.96m^2 * 2 = 3.14h_booth * 3
Simplifying:
7.92m^2 = 9.42h_booth m^3
Dividing both sides by 9.42m^3, we get:
7.92m^2 / 9.42m^3 = h_booth
Simplifying further, we find:
0.841m = h_booth
6. Substitute the value of h_booth back into the volume equations to find the volumes of the booths:
V_booth = 3.96m^2 * h_booth
= 3.96m^2 * 0.841m
= 3.33m^3
V_cylindrical booth = 3.14h_booth m^3
= 3.14 * 0.841m
= 2.645m^3
Therefore, the level of milk in the rectangular booth is approximately 3.33 cubic meters, while the level of milk in the cylindrical booth is approximately 2.645 cubic meters.
To find the level of milk in each vessel, we'll need to calculate the volumes of the cylindrical tank and the cylindrical vessel.
1. Calculating the volume of the cylindrical tank:
The diameter of the cylindrical tank is given as 2m, which means the radius is half of that, i.e., 1m.
And the height of the tank is given as 4.2m.
The formula for the volume of a cylinder is: V = πr^2h
Plugging in the values, we have:
V_tank = π * (1m)^2 * 4.2m
V_tank = 4.2π cubic meters (This is the volume of milk in the cylindrical tank).
2. Calculating the volume of the cylindrical vessel:
The diameter of the cylindrical vessel is given as 2m, so the radius is 1m.
Again, using the formula for the volume of a cylinder, we have:
V_vessel = π * (1m)^2 * h_vessel
We need to find the height of the cylindrical vessel. To do that, we'll use the ratio of supply between the two booths, which is 3:2. This means the ratio of the volumes of milk in the two vessels is also 3:2.
Given that the rectangular base area of the first booth is 3.96 sq. m, we can calculate its height using the formula for the area of a rectangle: A = l * w
3.96 = l * w
w = 3.96 / l
Since the base of the cylindrical vessel is a circle with diameter 2m, its width is 2m. Thus, the height of the cylindrical vessel is 3.96 / 2 = 1.98m.
Plugging in the values, we have:
V_vessel = π * (1m)^2 * 1.98m
V_vessel = 1.98π cubic meters (This is the volume of milk in the cylindrical vessel).
3. Calculating the levels of milk in each vessel:
To find the levels of milk, we'll equate the volumes to the areas of the respective bases.
Let the level of milk in the cylindrical tank be h_tank and in the cylindrical vessel be h_vessel.
Since the base area of the cylindrical tank is π(1m)^2 = π square meters, we can write:
h_tank = V_tank / π
Similarly, since the base area of the cylindrical vessel is π(1m)^2 = π square meters, we can write:
h_vessel = V_vessel / π
Plugging in the calculated values, we have:
h_tank = (4.2π) / π = 4.2 meters
h_vessel = (1.98π) / π = 1.98 meters
Therefore, the level of milk in the cylindrical tank is 4.2 meters, and the level of milk in the cylindrical vessel is 1.98 meters.