Surface Area of the simple figure
There is a question which states
The solid brick figure shown is made of small bricks of side 1. When the large brick is disassembled into its component small bricks , the total surface area of all small bricks is how much greater than surface area of larger brick
Here is how I am attempting it:
Surface Area of Large Brick = $6x^2=6(2)^2=24$
Surface Area of 1 small Brick = $6x^2=6(1)^2=6$
Total Small Bricks = 12 = So Total Surface Area = $72$
Difference = $72-24=48$
But the difference is suppose to be $40$. How ?
(EDIT : Image Edited)
$\endgroup$ 42 Answers
$\begingroup$For the brick you've drawn, the large brick has two $3\times3$ faces and four $2\times 3$ faces, so its surface area is $2(9)+4(6)=42$.
There are $3\times3\times2 = 18$ smaller bricks, each of which has surface area $6$ so the total surface area of the $18$ small bricks is $18(6)=108$.
The difference of the areas, then, is $108-42=66$.
On the other hand, if the brick has dimension $2\times2\times3$, then the large brick has two $2\times2$ faces and four $2\times 3$ faces, so its surface area is $2(4)+4(6)=32$.
There are $2\times2\times3 = 12$ smaller bricks, each of which has surface area $6$ so the total surface area of the $12$ small bricks is $12(6)=72$.
The difference of the areas, then, is $72-32=40$. This is likely what the original problem was, as mentioned in the comments.
$\endgroup$ 1 $\begingroup$SA of larger bricks is $$2LW+2LH+2HW = 2(3)(2)+2(3)(2)+(2)(2)(2)=12+12+8= 32 $$ because it is not a perfect cube, but it's a rectangular prism.
SA of smaller bricks $= 6\cdot 12 = 72$. Then, the difference = larger - smaller $ = 72-32 = 40$.
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