Surface area

Geometry Level 3

Find a polynomial expression for the surface area of the cube.

x 3 + 9 x 2 + 27 x + 27 x^3 + 9x^2 + 27x + 27 6 x 2 + 36 x + 54 6x^2 + 36x + 54 x 2 + 6 x + 9 x^2 + 6x + 9 6 x 2 + 6 x + 9 6x^2 + 6x + 9

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Munem Shahriar
Jun 7, 2017

Each face of the cube is a square of length ( x + 3 ) (x + 3)

The area of each square,

= ( x + 3 ) ( x + 3 ) = (x + 3)(x + 3)

= x ( x + 3 ) + 3 ( x + 3 ) = x(x + 3) + 3(x + 3)

= x 2 + 3 x + 3 x + 9 = x^2 + 3x + 3x + 9

= x 2 + 6 x + 9 = x^2 + 6x + 9

Now,

The cube has six such faces

The total surface area of the cube,

= 6 × = 6 \times The area of one face

= 6 ( x 2 + 6 x + 9 ) = 6(x^2 + 6x + 9)

= 6 x 2 + 36 x + 54 = 6x^2 + 36x + 54

Area of a square: ( x + 3 ) ( x + 3 ) = ( x + 3 ) 2 Using the identity ( x + y ) 2 = x 2 + 2 x y + y 2 = x 2 + 6 x + 9 (x + 3)(x +3) = (x + 3)^2 \color{#3D99F6} \text{ Using the identity } (x + y)^2 = x^2 + 2xy + y^2\color{#D61F06} \implies = x^2 + 6x + 9

There are 6 squares so: 6 × ( x 2 + 6 x + 9 ) 6 x 2 + 36 x + 54 6 \times (x^2 + 6x + 9) \implies \color{#69047E} 6x^2 + 36x + 54

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...