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 posture lie flat in the box?

Answer 1

Answer: Yes, the posture will be lie flat in the box.

Explanation:

since we have given that

Area of square framed poster = 9 sq. feet

Volume of cube shaped box = 30 cubic feet.

As we know the formula for "volume of cube":

`Volume=30\\\\a^3=30\\\\a=\sqrt[3]{30}=3.10\ feet`

So, Area of cube shaped box would be

`6a^2=6* (3.1)^2=57.9\ ft^2`

Since the cube box is large enough so that the posture will lie flat in the box.

Answer 2

We calculate for the dimensions (the length of the sides) of both the poster and the cube. If the length of the side of the poster is shorter compared to that of the box then, the poster will lie flat in the cube. However, if the poster has a length that is longer than that of the cube then, it will not lie flat in the cube.

length of the poster = sqrt (9 ft^2) = 3 ft
length of the cube = cbrt (30 ft^3) = 3.11 ft

Since, the length of the cube is longer compared to the length of the poster then, the poster will lie flat on the cube.