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The surface area of a cube is 294 square inches. A hole is cut out of the cube as shown. What is the surface area of the new solid?

The surface area of a cube is 294 square inches. A hole is cut out of the cube as-example-1
User Sparragus
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1 Answer

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Explanation:

this might be an intended trick question.

it suggests that the only difference for the surface area are the missing 2 small rectangles at the top and bottom areas.

while that is a difference, yes, we have now also the inner walls of the holes as additional surface area !

let's start with the subtraction of the 2 hole areas :

each cut-out rectangle is 1.5×2 in² = 3 in²

so, both together are 2×3 = 6 in²

and now for the additional inner walls :

first we need to find the dimensions of the cube.

as a cube, all sidelines are of equal length, and each side area is a square.

it has 6 side areas:

294 / 6 = 49 in²

each side area is a square of 49 in².

and that means each side is sqrt(49) = 7 in long.

therefore, the height of the inner walls is also 7 in.

now we know for the inner walls of the hole :

2 are 1.5×7 in² = 10.5 in²

2 are 2×7 in² = 14 in²

that makes the new surface area

294 - 6 + 2×10.5 + 2×14 = 288 + 21 + 28 = 337 in²

User Noralba
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