Question

a fish tank is in the shape of a cube. the volume of the tank is 64 cubic feet. what is the width, in inches, of one side of the fish tank? 192 inches 96 inches 48 inches 256 inches

Explanation:

Step1: Recall the volume formula for a cube

The volume \( V \) of a cube with side length \( s \) is given by \( V = s^3 \). Also, we need to convert the volume from cubic feet to cubic inches. We know that \( 1 \) foot \( = 12 \) inches, so \( 1 \) cubic foot \( = 12^3=1728 \) cubic inches.

Step2: Convert the volume to cubic inches

The volume of the tank is \( 64 \) cubic feet. So in cubic inches, it is \( 64\times1728 \) cubic inches. Let's calculate that: \( 64\times1728 = 110592 \) cubic inches.

Step3: Find the side length of the cube

Since \( V = s^3 \), we need to find \( s \) such that \( s^3=110592 \). Let's check the options. Let's check each option:

• For \( s = 48 \): \( 48^3=48\times48\times48 = 2304\times48 = 110592 \).
• For \( s = 96 \): \( 96^3=96\times96\times96 = 9216\times96 = 884736

eq110592 \)

• For \( s = 192 \): \( 192^3=192\times192\times192 = 36864\times192 = 7077888

eq110592 \)

• For \( s = 256 \): \( 256^3=256\times256\times256 = 65536\times256 = 16777216

eq110592 \)

So the side length (which is also the width) is \( 48 \) inches.

Answer:

48 inches