A cube has sides of length 5 cm. If one cube is attached along a face to another similar cube what is surface area new solid? How much area is lost?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The cube has sides with length 5 cm. The surface area of the cube is 6*5^2 = 6*25 = 150 cm^2.

When a similar cube is attached to the cube the total area of the new solid is 2*5^2 + 4*5*10 = 50 + 200 = 250 cm^2.

The total surface area of two cubes when they are separate is equal to 2*6*25 = 300 cm^2.

The area lost when the two cubes are combined and share a face is equal to 50 cm^2.

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to evaluate the total surface area of a cube such that:

`TSA = 6*A_square`

`TSA = 6*5^2 =gt TSA = 150 cm^2`

If the cubes are not attached, then the total surface area of two cubes is:

`TSA = 2*6*A_square = 12*A_square`

If you attach one cube to the next cube that has the same dimensions, the total surface area is:

`TSA_1= 4 *`  sides area`+ 2* A_square`

You need to evaluate the side area such that:

Side area `= 2*A_square`

`TSA_1 = 8*A_square + 2* A_square`

`TSA_1 = 10*A_square`

You need to evaluate the area lost when the cubes are combined:

`A lost = 12*A_square - 10*A_square`

A lost = `2*A_square = 2*25 = 50 cm^2`

Hence, evaluating the area lost when the two cubes are combined yields A lost = `50 cm^2` .

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