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6. A fish tank has dimensions 12 in x 27 in x 33 in.

a. Find the volume of this tank in cubic feet in two ways:

Approach I: Convert the dimensions of the tank to feet, and then find the volume of the tank in cubic feet.

Approach 2: Find the volume of the tank in cubic inches, and then convert the volume of the tank from cubic inches to cubic feet.

b. You have 20 gallons of fresh water to pour into the tank. Is this enough water to fill the tank? Use the fact that there are about 7.48 gallons in 1 cubic foot.

Answer :

To solve this problem, we will follow the two approaches as instructed to find the volume of the fish tank in cubic feet.

Approach 1: Convert dimensions to feet first

  1. Convert each dimension from inches to feet.

    • Length: [tex]12 \text{ inches} = \frac{12}{12} \text{ feet} = 1 \text{ foot}[/tex]
    • Width: [tex]27 \text{ inches} = \frac{27}{12} \text{ feet} = 2.25 \text{ feet}[/tex]
    • Height: [tex]33 \text{ inches} = \frac{33}{12} \text{ feet} \approx 2.75 \text{ feet}[/tex]

  2. Calculate the volume in cubic feet using the converted dimensions.
    [tex]\text{Volume} = 1 \text{ ft} \times 2.25 \text{ ft} \times 2.75 \text{ ft} = 6.1875 \text{ cubic feet}[/tex]

Approach 2: Calculate volume in cubic inches and convert to cubic feet

  1. Calculate the volume in cubic inches.
    [tex]\text{Volume} = 12 \text{ in} \times 27 \text{ in} \times 33 \text{ in} = 10692 \text{ cubic inches}[/tex]

  2. Convert cubic inches to cubic feet.

    • There are 1728 cubic inches in one cubic foot ([tex]12 \times 12 \times 12[/tex]).
      [tex]\text{Volume in cubic feet} = \frac{10692}{1728} \approx 6.1875 \text{ cubic feet}[/tex]

Both approaches confirm that the volume of the tank is approximately 6.1875 cubic feet.

b. Checking if 20 gallons is enough to fill the tank

  • The volume of the tank in cubic feet is approximately 6.1875 cubic feet.
  • There are approximately 7.48 gallons in 1 cubic foot.
  • Calculate the total capacity of the tank in gallons.
    [tex]\text{Capacity in gallons} = 6.1875 \text{ cubic feet} \times 7.48 \text{ gallons/cubic foot} \approx 46.26 \text{ gallons}[/tex]

Since the tank can hold approximately 46.26 gallons of water, the 20 gallons you have are not enough to fill it. You need more water to fill the tank completely.

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