Question

a cube container, with original volume 216 in³, is being redesigned to increase its capacity. the expression ( x^3 + 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 7.2... (options: in., in³, in²). type an integer or decimal rounded to the nearest tenth as needed.

Explanation:

Step1: Find the new volume

The original volume is \(216\space\text{in}^3\) and the volume can increase by a maximum of \(144\space\text{in}^3\). So the new volume \(V = 216 + 144=360\space\text{in}^3\).

Step2: Recall the volume formula for a cube

The volume of a cube with edge length \(s\) is \(V = s^3\). We need to find \(s\) such that \(s^3=360\). So we solve for \(s\) by taking the cube root of both sides: \(s=\sqrt[3]{360}\).

Step3: Calculate the cube root

Using a calculator, \(\sqrt[3]{360}\approx7.1699\). Rounding to the nearest tenth, we get \(7.2\).

Answer:

The maximum measurement of the edge of the larger cube is \(7.2\) in.