For a display, identical cubic boxes are stacked in square layers. Each layer consists of cubic boxes arranged in rows that form a square, and each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it. If the bottom layer has 81 boxes and the taop layer has only 1 box, how many boxes are in the display?

Answer:285  boxes are in the displayStep-by-step explanation:Given datatop layer box = 1last row box = 81to find out how many boxsolutionwe know that every row is a square so that if the bottom layer has 81 squares it mean this is 9² and every row has one lesser boxso that next row will have 8^2 and than 7² and so on till 1²so we can say that cubes in the rows as that Sum of all Squares = 9² + 8² +..........+ 1²Sum of Squares positive Consecutive Integers formula are Sum of Squares of Consecutive Integers = (1/6)(n)(n+1)(2n+1)   here n = 9 so equation will beSum of Squares of Consecutive Integers = (1/6) × (9) × (9+1) × (2×9+1) Sum of Squares of Consecutive Integers = 285so 285  boxes are in the display