Question Find the smallest inside length in meters of a cubical steel tank that holds 280 L of water, rounded to the nearest 0.01 m.

Studdy Solution

STEP 1

Assumptions
1. The tank is cubical, meaning all sides are of equal length.
2. The volume of the tank is $280 \mathrm{~L}$ .
3. $1 \mathrm{~L} = 0.001 \mathrm{~m}^3$ (conversion factor from liters to cubic meters).
4. The inside length of the tank is to be calculated in meters.
5. The result should be rounded to the nearest $0.01 \mathrm{~m}$ .

STEP 2

First, we need to convert the volume from liters to cubic meters using the conversion factor.
$Volume_{\mathrm{m}^3} = Volume_{\mathrm{L}} \times Conversion\, factor$

STEP 3

Now, plug in the given volume in liters and the conversion factor to calculate the volume in cubic meters.
$Volume_{\mathrm{m}^3} = 280 \mathrm{~L} \times 0.001 \mathrm{~m}^3/\mathrm{L}$

STEP 4

Calculate the volume in cubic meters.
$Volume_{\mathrm{m}^3} = 280 \times 0.001 = 0.28 \mathrm{~m}^3$

STEP 5

Since the tank is cubical, all sides are of equal length. We can find the length of one side by taking the cube root of the volume.
$Side\, length = \sqrt[3]{Volume_{\mathrm{m}^3}}$

STEP 6

Plug in the value for the volume in cubic meters to calculate the side length.
$Side\, length = \sqrt[3]{0.28 \mathrm{~m}^3}$

STEP 7

Calculate the side length.
$Side\, length = \sqrt[3]{0.28} \approx 0.65 \mathrm{~m}$

STEP 8

Round the side length to the nearest $0.01 \mathrm{~m}$ .
$Side\, length \approx 0.65 \mathrm{~m}$
Since $0.65$ is already at the $0.01 \mathrm{~m}$ precision, no further rounding is needed.
The smallest possible inside length of the tank is approximately $0.65 \mathrm{~m}$ .

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