Question

talía 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 68 cubic feet. will the poster lie flat in the box? explain. an area of 16 square feet means the square poster has dimensions 4 ft x 4 ft. if the poster were the side of a cube, that cube would have a volume of ft³. the box has a smaller volume, so its sides must be larger than the sides of the poster, meaning that the poster would lie flat in the bottom of the box.

Explanation:

Step1: Recall volume formula for cube

The volume formula for a cube is $V = s^{3}$, where $s$ is the side - length of the cube. If the side - length of the cube is the same as the side of the poster ($s = 4$ feet), then $V=4^{3}$.

Step2: Calculate the volume

$4^{3}=4\times4\times4 = 64$ cubic feet.

Step3: Compare with box volume

The box has a volume of 68 cubic feet. Since 64 < 68 and the side - length of the cube corresponding to the poster's side is 4 feet, and the box can accommodate a cube of side - length greater than 4 feet (because its volume is greater than the volume of a 4 - foot side - length cube), the poster will lie flat in the box.

Answer:

Yes, because if the side of a cube equal to the side of the poster (4 feet) has a volume of 64 cubic feet which is less than the volume of the box (68 cubic feet), meaning the box has sides large enough for the poster to lie flat.