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A rectangular prism has the following dimensions. The base has sides that are 6 cm and 7 cm and the height is 9 cm. How many squares with 1 cm edges can cover the entire surface area of the prism with no overlaps?

User Dan Getz
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1 Answer

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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.

User Dunaevsky Maxim
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