Question

You are painting the outside of a jewelry box, including the bottom. To find the surface area (S.A.) of the jewelry box, you can use the formula S.A. = 2wl + 2lh + 2wh , where l is the length, w is the width, and h is the height. What is the surface area of the jewelry box in terms of x ?

Answer 1

1) The radius would be r = x + 4y 

.... and the area would be A = pi ( x + 4y )^2 

2) x is not defined. You have to state the relationship of x with l ,w, and, h 

3) The square prism is a cube. I assume that the edge is x. Then the perimeter of any one face is : 

... p = 4x

Answer 2

The surface area of a shape is the amount of space it covers.

The surface area of the jewelry box is: $S.A =38x^2+ 38x$

From the complete question, the dimension of the box is:

$l = 2x+5$

$w= x$

$h= x+3$

So, the surface area is:

$S.A = 2wl + 2lh + 2wh$

$S.A =2 \times x \times (2x + 5) + 2 \times (2x + 5) \times (x + 3) + 2 \times x \times (x + 3)$

Open brackets

$S.A =2 \times (2x^2 + 5x) + 2 \times (2x^2 + 5x + 6x + 15) + 2 \times (x^2 + 3x)$

$S.A =2 \times (2x^2 + 5x) + 2 \times (2x^2 + 11x + 15) + 2 \times (x^2 + 3x)$

Factor out 2

$S.A =2 \times [(2x^2 + 5x + 2x^2 + 11x + 15x^2 + 3x)]$

Collect like terms

$S.A =2 \times [(2x^2 + 2x^2+ 15x^2+ 5x + 11x + 3x)]$

$S.A =2 \times [(19x^2+ 19x)]$

Open brackets

$S.A =38x^2+ 38x$

Hence, the surface area of the box is $S.A =38x^2+ 38x$

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