Question

question 3
several glass aquariums of various sizes are for sale at a pet shop. they are all shaped like rectangular prisms
a 15 - gallon tank is 24 inches long, 12 inches wide, and 12 inches tall

1. match the dimensions of the other tanks with the volume of water they can each hold.

column a

1. 36 inches long, 18 inches wide, and 12 inches tall
2. 16 inches long, 10 inches wide, and 8 inches tall
3. 30 inches long, 12 inches wide, and 12 inches tall
4. 20 inches long, 12 inches wide, and 10 inches tall

column b
a. 10 gallons
b. 20 gallons
c. 30 gallons
d. 5 gallons

Explanation:

First, we use the given 15-gallon tank to find the conversion factor between cubic inches and gallons.

Step1: Calculate 15-gal tank volume

$\text{Volume} = 24 \times 12 \times 12 = 3456$ cubic inches

Step2: Find gal per cubic inch

$\text{Conversion factor} = \frac{15}{3456} = \frac{5}{1152}$ gallons per cubic inch
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Step3: Calculate Tank 1 volume

$\text{Volume}_1 = 36 \times 18 \times 12 = 7776$ cubic inches

Step4: Find Tank 1 capacity

$\text{Capacity}_1 = 7776 \times \frac{5}{1152} = 33.75 \approx 30$ gallons (matches c)
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Step5: Calculate Tank 2 volume

$\text{Volume}_2 = 16 \times 10 \times 8 = 1280$ cubic inches

Step6: Find Tank 2 capacity

$\text{Capacity}_2 = 1280 \times \frac{5}{1152} \approx 5.56 \approx 5$ gallons (matches d)
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Step7: Calculate Tank 3 volume

$\text{Volume}_3 = 30 \times 12 \times 12 = 4320$ cubic inches

Step8: Find Tank 3 capacity

$\text{Capacity}_3 = 4320 \times \frac{5}{1152} = 18.75 \approx 20$ gallons (matches b)
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Step9: Calculate Tank 4 volume

$\text{Volume}_4 = 20 \times 12 \times 10 = 2400$ cubic inches

Step10: Find Tank 4 capacity

$\text{Capacity}_4 = 2400 \times \frac{5}{1152} \approx 10.42 \approx 10$ gallons (matches a)

Answer:

1. c. 30 gallons
2. d. 5 gallons
3. b. 20 gallons
4. a. 10 gallons