Answer:
486 squares with 1 cm edges can cover the entire surface area of the prism with no overlaps.
Explanation:
To find the surface area of the rectangular prism, we need to find the area of each face and add them together. There are six faces to a rectangular prism: top, bottom, front, back, left, and right. Since the top and bottom faces have the same dimensions, we only need to find the area of one of them and double it.
Area of top/bottom face = length * width
= 6 cm * 7 cm
= 42 cm^2
Area of front/back face = length * height
= 6 cm * 9 cm
= 54 cm^2
Area of left/right face = width * height
= 7 cm * 9 cm
= 63 cm^2
Total surface area = 2(top/bottom face) + 2(front/back face) + 2(left/right face)
= 2(42 cm^2) + 2(54 cm^2) + 2(63 cm^2)
= 252 cm^2 + 108 cm^2 + 126 cm^2
= 486 cm^2
To find the number of 1 cm squares that can cover the surface area of the prism, we can divide the total surface area by the area of one square:
Number of squares = Surface area / Area of one square
= 486 cm^2 / 1 cm^2
= 486
So, 486 squares with 1 cm edges can cover the entire surface area of the prism with no overlaps.