a cubic container was completely filled with water. when 3/4 of the water from the container was poured into a rectangular tank, the tank became 1/4 full. the capacity of the tank is 1.024 liters more than that of the cubic container. Find the length of the cubic container
Hard to read.
3/4 * V=1/4(1.024 + V) is what I read.
solve for V
Then length^3=V or
length= cuberoot (V)
Let's assume the length of the cubic container is "x" units.
Given that 3/4 of the water was poured into the rectangular tank and it became 1/4 full, we can conclude that 1/4 of the water originally in the cubic container is 1/4 of the capacity of the tank.
So, the capacity of the rectangular tank is (1/4) * (3/4) = 3/16 of the capacity of the cubic container.
Now, we are given that the capacity of the tank is 1.024 liters more than that of the cubic container. We can convert this into the same unit as the capacity of the cubic container.
1.024 liters is equal to 1024 cubic centimeters. The unit for capacity is cubic centimeters.
So, the capacity of the tank can be written as (3/16)x + 1024.
According to the question, this capacity is equal to the capacity of the cubic container.
Hence, (3/16)x + 1024 = x.
Multiplying both sides of the equation by 16 to eliminate the fraction, we get:
3x + 16384 = 16x.
Simplifying further, we get:
16x - 3x = 16384.
13x = 16384.
Dividing both sides by 13, we get:
x = 16384 / 13.
Therefore, the length of the cubic container is x = 1260 units.
To find the length of the cubic container, we need to systematically work through the information provided.
1. Let's start by assigning a variable to represent the length of the cubic container. Let's call it "x".
2. We know that the cubic container was completely filled with water. Therefore, its volume is given by x^3.
3. Next, we are told that 3/4 of the water from the cubic container was poured into a rectangular tank. This means that (3/4) * x^3 amount of water was poured into the tank.
4. We are also given that when (3/4) of the water from the container was poured into the tank, the tank became 1/4 full. This gives us the equation: (1/4) * tank_capacity = (3/4) * x^3.
5. We know that the capacity of the tank is equal to x^3 + 1.024. Therefore, we can rewrite the equation as: (1/4) * (x^3 + 1.024) = (3/4) * x^3.
6. Multiplying both sides of the equation by 4, we get: x^3 + 1.024 = 3 * x^3.
7. Simplifying the equation, we have: 1.024 = 2 * x^3.
8. Dividing both sides of the equation by 2, we get: x^3 = 0.512.
9. Taking the cube root of both sides, we find: x = 0.8.
Therefore, the length of the cubic container is 0.8 units.