Question

talía is packing a moving box. she has a square - framed poster with an area of 9 square feet. the cube - shaped box has a volume of 29 cubic feet. will the poster lie flat in the box? explain? an area of 9 square feet means the square poster has dimensions ft x ft. if the poster were the side of a cube, that cube would have a volume of ft³. the box has a volume, so its sides must be than the sides of the poster, meaning that the poster lie flat in the bottom of the box.

Explanation:

Step1: Find side - length of the poster

For a square poster with area $A = 9$ square feet, using the formula $A=s^2$ (where $s$ is the side - length of the square), we solve for $s$.
\[s=\sqrt{A}=\sqrt{9}=3\] feet.

Step2: Find side - length of the cube - shaped box

For a cube - shaped box with volume $V = 29$ cubic feet, using the formula $V = a^3$ (where $a$ is the side - length of the cube), we solve for $a$.
\[a=\sqrt[3]{V}=\sqrt[3]{29}\approx3.07\] feet.

Step3: Compare side - lengths

Since $\sqrt[3]{29}\approx3.07>3$, the side - length of the box is greater than the side - length of the poster.

Answer:

Yes, the poster will lie flat in the box because the side - length of the cube - shaped box ($\sqrt[3]{29}\approx3.07$ feet) is greater than the side - length of the square poster (3 feet).