This rectangular tank is partly filled with oil and water in ration 3:4. 9650cm3 of the tank is not filled. If the tank contains 420ml more water than oil, find the base area of the tank?
Let's call the volume of oil in the tank "o" and the volume of water "w". We know that:
o + w = total volume of tank - 9650
We also know that the ratio of oil to water is 3:4, which means that:
o/w = 3/4
We can use this information to create a system of equations. First, we can solve for o in the second equation:
o = (3/4)w
Next, we can substitute this expression for o into the first equation:
(3/4)w + w = total volume of tank - 9650
Simplifying this equation, we get:
(7/4)w = total volume of tank - 9650
Now we have an equation that relates the volume of water in the tank to the total volume and the amount of unfilled space. But we still need another equation to solve for the unknowns.
We're told that the tank contains 420ml more water than oil. Since we know that o = (3/4)w, we can write:
w = o + 420
Substituting the expression for o from above, we get:
w = (3/4)w + 420
Solving for w, we get:
w = 1680
Now we can use this value of w to find o:
o = (3/4)w
o = (3/4) * 1680
o = 1260
So the tank contains 1260ml of oil and 1680ml of water. To find the base area of the tank, we need to know the height of the tank. Let's call this "h". We can use the formula:
volume = base area * height
We know that the total volume of the tank is:
total volume = o + w + 9650
total volume = 1260 + 1680 + 9650
total volume = 12590
So we can write:
12590 = base area * h
We don't know the value of h, but we do know that the ratio of oil to water in the tank is 3:4, which means that the height of the oil layer is:
h_oil = (3/7) * h
And the height of the water layer is:
h_water = (4/7) * h
We also know that the base area of the tank is the same for both the oil and water layers. So we can write:
base area * h_oil = 1260
base area * h_water = 1680
Substituting the expressions for h_oil and h_water into these equations, we get:
base area * (3/7)h = 1260
base area * (4/7)h = 1680
Dividing these equations, we get:
(3/4) * base area = 1260/1680
(3/4) * base area = 3/4
base area = 3/4 * (1680/1260)
base area = 1
So the base area of the tank is 1 cm^2.
The volume of a fish tank is 7500 cm3. 1 out of 5 of it is filled with water. How much more water is needed to fill up the tank to make it 3 out of 4 full?
If 1 out of 5 of the tank is filled with water, then the amount of water in the tank is:
(1/5) * 7500 = 1500 cm^3
To make the tank 3 out of 4 full, we need to fill it with 3/4 - 1/5 = 11/20 of the total volume. So we need to find the volume of water required to fill up 11/20 of the tank.
The volume of 11/20 of the tank is:
(11/20) * 7500 = 4125 cm^3
To fill this volume with water, we need to add:
4125 - 1500 = 2625 cm^3
So we need to add 2625 cm^3 of water to the tank to make it 3 out of 4 full.
It said: 9650cm3 of the tank is not filled
The bot set up the equation as if the water and oil add up to 9650
so its answer cannot possibly be correct
You are correct, my apologies for the mistake. I misread the problem.
Let's start over. Given that the rectangular tank is partly filled with oil and water in a ratio of 3:4, we can set up two equations to represent the volume of oil and water in the tank:
Volume of Oil = 3x
Volume of Water = 4x
where x is a constant.
We also know that 9650 cm^3 of the tank is not filled, so we can set up another equation for the total volume of the tank as:
Total Volume of Tank = Volume of Oil + Volume of Water + Unfilled Volume
Total Volume = 3x + 4x + 9650
Total Volume = 7x + 9650
We are given that the tank contains 420 ml more water than oil, so we can set up another equation as:
Volume of Water = Volume of Oil + 420
4x = 3x + 420
x = 420
Now that we have found the value of x, we can substitute it back into the previous equations to find the volume of oil and water:
Volume of Oil = 3x = 3 * 420 = 1260 cm^3
Volume of Water = 4x = 4 * 420 = 1680 cm^3
To make the tank 3 out of 4 full, we need to fill it to 3/4 of its total volume. The current volume of liquid in the tank is 1260 + 1680 = 2940 cm^3.
Therefore, the total volume of the tank required to make it 3/4 full is:
(2940 / (3/4)) = 3920 cm^3
The amount of space left to fill is:
3920 - 2940 = 980 cm^3
We need to add the difference in the volume of water required to fill the remaining space:
(4/7) * 980 = 560 cm^3
Therefore, we need to add 560 cm^3 of water to the existing water volume of 1680 cm^3 to make the tank 3 out of 4 full.
To solve this problem, we can break it down into two steps:
Step 1: Calculate the volume of the tank
Step 2: Use the given information to find the base area of the tank
Let's start with Step 1:
Step 1: Calculate the volume of the tank
Let's assume the base area of the tank is A cm^2 and the height of the tank is h cm. Then the volume of the tank can be calculated using the formula: Volume = base area * height.
Now, let's move on to Step 2:
Step 2: Use the given information to find the base area of the tank
According to the problem, the ratio of oil to water in the tank is 3:4. This means that the volume of oil is 3 parts and the volume of water is 4 parts.
Let's calculate the volume of oil and the volume of water separately:
Volume of oil = (3/7) * Volume of tank
Volume of water = (4/7) * Volume of tank
We are also given that 9650 cm^3 of the tank is not filled. This means that the sum of the volume of oil and the volume of water is equal to the volume of the tank minus 9650 cm^3:
Volume of oil + Volume of water = Volume of tank - 9650 cm^3
Since we know that the volume of water is 420 ml (converted to cm^3) more than the volume of oil, we can write:
Volume of water = Volume of oil + 420 cm^3
Now, let's substitute these values into the equation above:
(3/7) * Volume of tank + (4/7) * Volume of tank = Volume of tank - 9650 cm^3
(4/7) * Volume of tank - (3/7) * Volume of tank = 420 cm^3
Simplifying this equation, we get:
(1/7) * Volume of tank = 420 cm^3
Finally, to find the base area of the tank, we divide the volume of the tank by its height:
Volume of tank = base area * height
Substituting the volume of the tank into the equation above, we get:
(1/7) * (base area * height) = 420 cm^3
Now we can solve for the base area of the tank:
base area = (420 cm^3 * 7) / height
Unfortunately, we are missing the information about the height of the tank, so it is not possible to find the exact base area of the tank without that information.