Question

talia is packing a moving box. she has a square - framed poster with an area of 16 square feet. the cube - shaped box has a volume of 69 cubic feet. will the poster lie flat in the box? explain. an area of 16 square feet means the square poster has dimensions ft× 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 square poster

The area of a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length. Given $A = 16$ square feet, we solve for $s$:
$ s^{2}=16$, so $s=\sqrt{16}=4$ feet.

Step2: Find the side - length of the cube if the poster is its side

If the side of the cube is the same as the side of the poster ($s = 4$ feet), the volume of a cube is $V=s^{3}$. Then $V = 4^{3}=64$ cubic feet.

Step3: Compare the volume of the cube (if poster is a side) and the box

The box has a volume of 69 cubic feet. Since $64<69$ and the side - length of the poster is 4 feet, the poster will lie flat in the box because the dimensions of the base of the box (assuming it can accommodate a 4 - foot side) are large enough.

Answer:

The dimensions of the square poster are 4 ft×4 ft. If the poster were the side of a cube, that cube would have a volume of 64 $ft^{3}$. The box has a volume of 69 $ft^{3}$, so the poster will lie flat in the box.