Question

talita 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? 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 would lie flat in the bottom of the box.

Explanation:

Step1: Find side - length of the poster

Let the side - length of the square poster be $s$. The area of a square is $A = s^{2}$. Given $A = 9$ square feet, then $s^{2}=9$, so $s = 3$ feet (since $s>0$).

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

Let the side - length of the cube - shaped box be $a$. The volume of a cube is $V=a^{3}$. Given $V = 30$ cubic feet, then $a=\sqrt[3]{30}\approx3.11$ feet.

Step3: Compare side - lengths

Since $3.11>3$, 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 ($\sqrt[3]{30}\approx3.11$ feet) is greater than the side - length of the square poster (3 feet).