Question

a cube container, with original volume 216 in³, is being redesigned to increase its capacity. the expression x + 216 in³ models the volume of the new cube. if the volume can increase by a maximum of 144 in³, what is the maximum measurement of the edge of the larger cube? the maximum measurement of the edge of the larger cube is (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Determine the new volume

The original volume is \(216\) in³, and the maximum increase in volume \(x\) is \(144\) in³. So the new volume \(V\) is the sum of the original volume and the increase:
\(V = 216 + 144 = 360\) in³.

Step2: Find the edge length of the cube

The volume \(V\) of a cube with edge length \(s\) is given by the formula \(V = s^3\). We need to find \(s\) when \(V = 360\). So we solve the equation \(s^3 = 360\) for \(s\). Taking the cube root of both sides, we get:
\(s=\sqrt[3]{360}\)

Calculating the cube root of \(360\): \(\sqrt[3]{360}\approx7.1699\). Rounding to the nearest tenth, we get \(s\approx7.2\).

Answer:

\(7.2\)