A hydraulic reservoir is to be made to hold 1000L but due to space restrictions the area available is 800mm x 1100mm.

What height would the tank have to be in mm ?

To find the height of the tank, we need to use the formula for the volume of a rectangular tank:

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]

Given:
- Volume (\( V \)) = 1000 liters = 1000,000 cubic millimeters (since 1 liter = 1,000,000 mm³)
- Length (\( L \)) = 800 mm
- Width (\( W \)) = 1100 mm

We need to find the height (\( H \)).

Using the formula:

\[
H = \frac{V}{L \times W}
\]

Substituting the values:

\[
H = \frac{1,000,000 \, \text{mm}^3}{800 \, \text{mm} \times 1100 \, \text{mm}}
\]

Let's calculate it.

\[
H = \frac{1,000,000}{880,000} \approx 1.136 \text{ mm}
\]

It looks like I made a mistake in the previous step. I was calculating it wrong. Let's go back and try again.

The correct value of height (\( H \)) would be:

\[
H = \frac{1,000,000}{880,000} \approx 1.136 \text{ meters } = 1,136 \text{ mm}
\]

So, the height of the tank needs to be approximately 1,136 mm to hold 1000 liters.

Do you want more details, or have any questions?

Here are 5 related questions for further exploration:
1. How would the height change if the volume was increased to 1500 liters?
2. What would the height be if the length and width were swapped?
3. How would the height differ if the area was reduced to 700mm x 1000mm?
4. What material would be suitable to construct a hydraulic reservoir of this size?
5. How does temperature affect the volume capacity of the reservoir?

**Tip:** Always check unit conversions, especially when working with large volumes or different units like liters and cubic millimeters.

Learn how to calculate the height of a hydraulic reservoir to hold 1000 liters, given a constrained area of 800mm x 1100mm. Use our step-by-step solution using the volume formula for a rectangular tank. Suitable for students in Grades 7-9.

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