Question

1. higher order thinking talia 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. the volume of the cube - shaped box is 30 cubic feet.

Explanation:

Step1: Find side - length of poster

Since the poster is square - framed and has an area $A = 9$ square feet. Let the side - length of the poster be $s_1$. Using the formula for the area of a square $A=s_1^2$, we have $s_1=\sqrt{9}=3$ feet.

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

Let the side - length of the cube - shaped box be $s_2$. The volume of a cube is $V = s_2^3$, and $V = 30$ cubic feet. So, $s_2=\sqrt[3]{30}\approx3.11$ feet.

Step3: Compare side - lengths

Since $s_1 = 3$ feet and $s_2\approx3.11$ feet, and $3<3.11$.

Answer:

Yes, the poster will lie flat in the box because the side - length of the square - framed poster ($3$ feet) is less than the side - length of the cube - shaped box (approximately $3.11$ feet).