Question

In the following sequence, the figures are made of cubes that are glued together. If the exposed surface needs to be painted, how many squares will be painted in (a) the 15th figure? (b) the nth figure?"
squares painted
a. The 15th figure will have
(Type a whole number)

Answer 1

A standard solid with six square faces, in Euclidean Geometry; that is a normal hexahedron. Themes connected: Polyhedron. Since a cube's volume is represented, the cube of that quantity is called in arithmetic and algebra, in terms of edge e, and $e^3$, and the further calculation can be defined as follows:

• When there is 1 cube then the number of surfaces$\bold{=6}$
• When there is 2 cube then the number of surfaces $\bold{=6 \times 2-2}$
• When there is 3 cube then the number of surfaces $\bold{=6 \times 3-2\times 2}$

So, when n cubes are there

$\to \bold{=6\times n-2(n-1)}$

   $\bold{=6n-2n+2}\\\\\bold{= 4n+2}$

when n=15 then:

$\to \bold{=6\times 15-2(15-1)}$

   $\bold{=90-30 +2}\\\\\bold{=60+2}\\\\ \bold{=62}$

So, the final answer is "62 and 4n+2".

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