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 ?

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 Link

MrRoyal MrRoyal · Answer 2 · 2021-09-30T07:12:40-04:00

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 \(S.A =38x^2+ 38x\)