Question

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*

Answer 1

Since the box is cube-shaped, its volume is V = 30 ft^2 = s^3, where s is the length of one side. Then s = ∛30, or approx. 3.11 ft. The length of one side of the 9 ft^2 square poster is √9, or 3 ft. Yes, the 3 ft^2 poster will fit the box, whose bottom area is 3.11 ft^2.

Answer 2

Yes, the poster lie flat in the box.

Explanation:

Consider the provided information.

Talia is packing a moving box. She has a square-framed poster with an area of 9 square feet.

The area of square = (side)²

Thus, the side of the poster frame is:

9 = (side)²

√9 = side

side = 3

Take positive value as side should be a positive number.

The side of the poster frame is 3 feet.

The cube-shaped box has a volume of 30 cubic feet.

Volume of cube = (side)³

Thus, the side of cube-shaped box is:

30 = (side)³

∛30 = side

side ≈ 3.12

The side of cube-shaped box 3.12 feet.

3.12 feet is greater than 3 feet. That means the side of the cube shaped box is greater than side of the poster frame.

Hence, the poster lie flat in the box.