rectangular tank X measuring 50cm by 40cm by 10cm contains water to a height of 3 cm. The ratio of water in tank X to tank Y is 1:3.Tank Y has a square base of 1600cm squared. Calculate the height of water level in tank Y

We can solve this by calculating the volume of water in Tank X and then using the given ratio to determine the height of water in Tank Y.

### Step 1: Calculate the volume of water in Tank X.
Tank X is a rectangular tank with dimensions 50 cm by 40 cm by 10 cm. However, the water is only 3 cm high.

The volume of water in Tank X is:
\[
\text{Volume of water in Tank X} = \text{length} \times \text{width} \times \text{height of water}
\]
\[
= 50 \, \text{cm} \times 40 \, \text{cm} \times 3 \, \text{cm}
= 6000 \, \text{cm}^3
\]

### Step 2: Use the ratio to find the volume of water in Tank Y.
The ratio of the volume of water in Tank X to the volume of water in Tank Y is 1:3, meaning Tank Y has three times the volume of water as Tank X.

\[
\text{Volume of water in Tank Y} = 3 \times \text{Volume of water in Tank X}
\]
\[
= 3 \times 6000 \, \text{cm}^3
= 18000 \, \text{cm}^3
\]

### Step 3: Calculate the height of the water in Tank Y.
Tank Y has a square base of area 1600 cm². Let \( h \) be the height of the water level in Tank Y. The volume of water in a tank is given by:
\[
\text{Volume of water in Tank Y} = \text{base area} \times \text{height of water}
\]
\[
18000 = 1600 \times h
\]

Solve for \( h \):
\[
h = \frac{18000}{1600} = 11.25 \, \text{cm}
\]

### Final Answer:
The height of the water level in Tank Y is \( 11.25 \, \text{cm} \).

Would you like more details or have any questions?

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Here are some related questions for practice:

1. If the height of water in Tank X increased to 5 cm, what would be the new water height in Tank Y?
2. What would be the volume of water in Tank X if it was filled completely?
3. How much more water needs to be added to Tank X to reach its full capacity?
4. What is the surface area of Tank Y’s base?
5. If the base of Tank Y was rectangular instead of square, how would this affect the water height calculation?

**Tip**: Always ensure that units are consistent when calculating volume!

rectangular tank X measuring 50cm by 40cm by 10cm contains water to a height of 3 cm. The ratio of water in tank X to tank Y is 1:3. Tank Y has a square base of 1600 cm squared. Calculate the height of water level in tank Y.

Learn how to calculate the height of water in Tank Y when given the dimensions of Tank X and a water ratio of 1:3. This problem covers volume calculations, ratios, and the use of base area to determine the water height in Tank Y. Suitable for Grades 6-8 students.

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