Question

Five cubes are lined up in norder of size to form a solid. the side of each smaller cube is completely touching the side of the adjacent larger cube. The side lengths of the cubes are 1ft , 2ft, 3ft , 4ft, and 5ft. What is the surface area of the solid?.

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Answer 1

246 Square Feet

Explanation:

The cubes are of side length 1ft , 2ft, 3ft , 4ft, and 5ft in that order.

If the side of each smaller cube is completely touching the side of the adjacent larger cube.

• In the first and last cubes, 5 sides out of 6 are visible, so we use the formula
  `5l^2` for their surface area.

• In the 2nd, 3rd and 4th cubes, only 4 sides out of 6 are visible, so we use the formula
  `4l^2` for their surface area.

Surface Area of the Solid
`= 5(l_1)^2+4(l_2)^2+4(l_3)^2+4(l_4)^2+5(l_5)^2, where \: l_1,l_2,l_3,l_4,l_5`

are the length of the cubes in that order

Surface Area of the Solid

`= 5(1)^2+4(2)^2+4(3)^2+4(4)^2+5(5^2)\\=5+16+36+64+125\\=246 \:Square\: feet`