Question

talia is packing a moving box. she has a poster with an area of 9 square feet. the cube - shaped box has a volume of 30 cubic feet. will the poster lie flat in the box? explain. the volume of the cube - shaped box is 30 cubic feet.

Explanation:

Step1: Find the side - length of the cube

For a cube with volume $V = 30$ cubic feet, using the formula $V = s^{3}$ (where $s$ is the side - length of the cube), we have $s=\sqrt[3]{30}\approx3.11$ feet.

Step2: Find the area of one face of the cube

The area of one face of a cube with side - length $s$ is $A = s^{2}$. Substituting $s=\sqrt[3]{30}$, we get $A = (\sqrt[3]{30})^{2}=\sqrt[3]{900}\approx9.65$ square feet.

Step3: Compare the areas

The area of the poster is 9 square feet and the area of one face of the cube is approximately 9.65 square feet. Since $9<9.65$, the poster will lie flat in the box.

Answer:

Yes, the poster will lie flat in the box because the area of one face of the cube - shaped box (approximately 9.65 square feet) is greater than the area of the poster (9 square feet).