(a) A rectangular gasoline tank can hold 41.0 kg of gasoline when full. What is the depth(m) of the tank if it is 0.400 m wide by 0.900 m long?

(b) What is the volume(gal) of the tank? (It is suitable for a passenger car.)

To find the depth (m) of the tank, we can use the formula for volume:

Volume = Length x Width x Depth

Given:
Length = 0.900 m
Width = 0.400 m
Gasoline mass = 41.0 kg

We can rearrange the formula to solve for Depth:

Depth = Volume / (Length x Width)

Now, let's calculate the depth:

(a) Depth calculation:
Depth = 41.0 kg / (0.900 m x 0.400 m)
Depth = 41.0 kg / 0.36 m²
Depth ≈ 113.89 kg/m²

Therefore, the depth of the tank is approximately 113.89 kg/m².

To find the volume of the tank in gallons (gal), we need to convert the volume from cubic meters (m³) to gallons.

1 cubic meter (m³) = 264.172 gallons

First, let's calculate the volume in cubic meters using the formula:

Volume = Length x Width x Depth

Given:
Length = 0.900 m
Width = 0.400 m
Depth = 113.89 kg/m²

(b) Volume calculation:
Volume = 0.900 m x 0.400 m x 113.89 kg/m²
Volume ≈ 40.92 m³

Now, let's convert the volume to gallons:

Volume in gallons = Volume in cubic meters x 264.172 gallons/m³
Volume in gallons = 40.92 m³ x 264.172 gallons/m³
Volume in gallons ≈ 10,800.10 gallons

Therefore, the volume of the tank is approximately 10,800.10 gallons.

To find the depth of the tank in meters and the volume of the tank in gallons, we can use the formula for volume which is:

Volume = length × width × depth

(a) To find the depth of the tank in meters:
Given:
Width = 0.400 m
Length = 0.900 m
Volume = 41.0 kg

We can rearrange the formula for volume to solve for depth:
Volume = length × width × depth
Rearranging for depth:
Depth = Volume / (length × width)

Plugging in the given values:
Depth = 41.0 kg / (0.900 m × 0.400 m)
Depth = 45.6 kg·m²

Therefore, the depth of the tank is 45.6 kg·m².

(b) To find the volume of the tank in gallons:
Since the given volume is in kilograms (kg), we need to convert it to liters (L) before converting it to gallons.

To convert from kilograms to liters, we need to know the density of the gasoline. Let's assume the density of gasoline is 0.74 kg/L.

Given:
Volume = 41.0 kg
Density of gasoline = 0.74 kg/L

We can use the formula:
Volume = Mass / Density

Plugging in the given values:
Volume = 41.0 kg / 0.74 kg/L
Volume ≈ 55.4 L

To convert from liters to gallons, we use the conversion factor of 1 gallon = 3.78541 liters.

Using the conversion:
Volume in gallons = 55.4 L × (1 gallon / 3.78541 L)
Volume in gallons ≈ 14.6 gallons

Therefore, the volume of the tank is approximately 14.6 gallons.

V =m /ρ =41/750 = 0.055 m³ =14.53 gallons

V=L•W•D= >
D=V/L•W = 0.055/0.4•0.9 =0.15 m