Question

a cube container, with original volume \\(27\text{ in.}^3\\), is being redesigned to increase its capacity. the expression \\(x + 27\text{ in.}^3\\) models the volume of the new cube. if the volume can increase by a maximum of \\(144\text{ in.}^3\\), 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:

Calculate the maximum volume of the new cube

$$ V_{\text{max}} = 27 + 144 = 171\text{ in.}^3 $$

Calculate the maximum edge length using the cube root

$$ s = \sqrt[3]{V_{\text{max}}} = \sqrt[3]{171} \approx 5.5505\text{ in.} $$

Round to the nearest tenth

$$ s \approx 5.6\text{ in.} $$

Answer:

The maximum measurement of the edge of the larger cube is <blank>5.6</blank>