Question

tala 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 30 cubic feet. will the poster lie flat in the box? explain? click the icon to view the moving box. an area of 9 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 poster

The area of a square is $A = s^2$, where $s$ is the side - length. Given $A = 9$ square feet, then $s=\sqrt{9}=3$ feet.

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

The volume of a cube is $V = a^3$, where $a$ is the side - length. Given $V = 30$ cubic feet, then $a=\sqrt[3]{30}\approx3.11$ feet (since $3.11^3=30.09$).

Step3: Compare side - lengths

Since $\sqrt[3]{30}\approx3.11>3$, the side of the box is longer than the side of the poster.

Answer:

An area of 9 square feet means the square poster has dimensions $3$ ft $\times$ $3$ ft. If the poster were the side of a cube, that cube would have a volume of $27$ ft³. The box has a greater volume, so its sides must be greater than the sides of the poster, meaning that the poster will lie flat in the bottom of the box.