Chapter 4.3, Problem 39WE

To determine

To calculate: The total surface area of the solid.

Answer to Problem 39WE

The total surface area of the solid is $46x^2$ .

Explanation of Solution

Given information:

The solid is provided below,

Formula used:

The total surface area is sum of area of all faces of a solid.

The area of rectangle with length l , width bis $A=lb$ .

The area of square with side sis $A=s^2$ .

Calculation:

Consider thesolid provided below,

Recall that the total surface area is sum of area of all faces of a solid.

There are 12 rectangles, 3 on each block of the solid.

Length of rectangle is $3x$ and width is $x$ .

Also, there are 10 square, 5 on top and 5 on bottom of solid with each side x .

Total surface area is area of 12 rectangles and 10 squares.

Apply it,

  $\begin{array}{c}\text{TSA}=12\left(3x\right)x+10x^2\\ =36x^2+10x^2\\ =46x^2\end{array}$

Thus, the total surface area of the solid is $46x^2$ .