Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Mar 22, 2024

Find the total volume of Tyler's two cube-shaped storage spaces, where the small space has volume $12 \mathrm{ft}^{3}$ and the side length of the large space is $s$ (ft).

STEP 1

1. The volume of a cube is given by the formula $V = s^3$ , where $s$ is the length of one side of the cube.
2. The volume of the small storage space is given as $12 \mathrm{ft}^{3}$ , which implies that the side length of the small storage space is $2 \mathrm{ft}$ because $2^3 = 8$ and not $12$ . This is a discrepancy that we will address in the solution.
3. The total volume of two spaces is the sum of their individual volumes.

STEP 2

1. Correct the assumption about the volume of the small storage space.
2. Express the volume of the large storage space in terms of $s$ .
3. Add the volumes of the large and small storage spaces to get the total volume.
4. Identify the correct expression that represents the total volume.

STEP 3

Correct the assumption about the volume of the small storage space by acknowledging that the volume is given directly as $12 \mathrm{ft}^{3}$ and does not need to be derived from the side length.

STEP 4

Express the volume of the large storage space using the formula for the volume of a cube.
$V_{\text{large}} = s^3$

STEP 5

Add the volume of the small storage space to the volume of the large storage space to find the total volume.
$V_{\text{total}} = V_{\text{large}} + V_{\text{small}}$ $V_{\text{total}} = s^3 + 12 \mathrm{ft}^{3}$

STEP 6

Identify the correct expression that represents the total volume among the given options.
The correct expression is:
$s^3 + 12$

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