A square picture frame has an area of 64 square inches. Joey had a box in the shape of a cube that has a volume of 729 cubic inches. Will the frame fit on the bottom of the box ?
dimension of cube: cubrt(729)=9x9x9
so will the square fit? side of square is sqrt(64)
the sides of the frame are 8 inches (√64)
the edges of the box are 9 inches (cube root 729)
To determine whether the square picture frame will fit on the bottom of the cube-shaped box, we need to compare their respective areas and volumes.
First, let's find the length of one side of the square picture frame. Since the frame is square-shaped, all sides are equal in length. We can find this length by taking the square root of the frame's area.
The area of the square picture frame is given as 64 square inches. Taking the square root of 64, we find that each side of the frame measures 8 inches.
Now, let's find the length of one side of the cube-shaped box. To do this, we need to find the cube root of the volume of the box.
The volume of the cube-shaped box is given as 729 cubic inches. Taking the cube root of 729, we find that each side of the box measures 9 inches.
Comparing the lengths of the sides, we see that the side length of the cube-shaped box (9 inches) is greater than the side length of the square picture frame (8 inches).
Since the side length of the cube-shaped box is larger than the side length of the square picture frame, we can conclude that the frame will fit on the bottom of the box.