SAT Ratios, Rates & Proportions Question 41 | Free SAT Prep | Aniko

00:00

Question 41·Medium·Ratios, Rates, Proportional Relationships, and Units

0 / 58

A cylindrical aquarium is completely filled with water and holds 47 gallons. Approximately how many cubic inches of water does the aquarium contain?

Use the following conversion factors:

$1\text{ gallon}=3.785\text{ liters}$
$1\text{ liter}=1{,}000\text{ cubic centimeters}$
$1\text{ inch}=2.54\text{ centimeters}$

Your answer

(Express the answer as an integer)

For unit-conversion questions, use dimensional analysis: write the starting quantity and multiply by conversion factors as fractions so that units cancel step by step. Track units carefully, especially with squared or cubed units—remember that if a length conversion uses a factor of $k$ , then an area conversion uses $k^2$ and a volume conversion uses $k^3$ . Combine all conversions into one clean expression, evaluate with your calculator, and then round only at the end to save time and reduce error.

Hints

Click me!

Start with gallons to liters

You are given 47 gallons and a gallon-to-liter conversion. What do you multiply 47 by to find the number of liters?

From liters to cubic centimeters

Once you know the volume in liters, use the fact that $1$ liter $=1{,}000$ cubic centimeters. How does that change the number?

Be careful with cubic units

You know $1$ inch $=2.54$ centimeters. For volumes, how many cubic centimeters are in $1$ cubic inch? Should you multiply or divide by $(2.54)^3$ to go from cubic centimeters to cubic inches?

Put all conversions together

Write one expression that starts with 47 and applies all three conversions in order. Then evaluate that expression and round reasonably.

Desmos Guide

Compute all conversions in one expression

In Desmos, type the single expression:

47 * 3.785 * 1000 / (2.54^3)

The output of this expression is the approximate number of cubic inches of water in the aquarium. Use that value, rounded to the nearest whole number, as your answer.

Step-by-step Explanation

Convert gallons to liters

Use the first conversion factor: $1$ gallon $=3.785$ liters.

So for $47$ gallons:

47 \times 3.785 = 177.895

The aquarium contains $177.895$ liters of water.

Convert liters to cubic centimeters

Use the second conversion factor: $1$ liter $=1{,}000$ cubic centimeters.

Multiply the liters by $1{,}000$ :

177.895 \times 1{,}000 = 177{,}895

So the volume is $177{,}895$ cubic centimeters.

Set up the conversion from cubic centimeters to cubic inches

Use the third conversion: $1$ inch $=2.54$ centimeters.

For volume, this means:

$1$ inch $=2.54$ cm
$1$ cubic inch $=(2.54)^3$ cubic centimeters

So:

1\text{ in}^3 = (2.54)^3\text{ cm}^3

To convert from cubic centimeters to cubic inches, divide by $(2.54)^3$ :

\text{cubic inches} = \frac{177{,}895}{(2.54)^3}

Calculate and approximate the final volume in cubic inches

First compute $(2.54)^3$ :

(2.54)^2 = 6.4516,

6.4516 \times 2.54 \text{ (which is }2.54^3\text{)} \[4pt] \approx 16.387064

Now divide the cubic centimeters by this value:

\frac{177{,}895}{16.387064} \approx 10{,}855.9

Rounding to the nearest whole number gives about $10{,}856$ cubic inches.

So, the aquarium contains approximately 10,856 cubic inches of water.

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation