Chapter 4.3, Problem 38WE

To determine

To calculate: The total surface area of the solid.

Answer to Problem 38WE

The total surface area of the solid is $22a^2$ .

Explanation of Solution

Given information:

The solid is provided below,

Formula used:

The total surface area of a cuboid with length l , width b and height his $\text{TSA}=2\left(lb+bh+hl\right)$ .

Calculation:

Consider thesolid provided below,

Recall that the total surface area of a cuboid with length l , width b and height his $\text{TSA}=2\left(lb+bh+hl\right)$ .

Here, $l=3a,b=2a\text{ and }h=a$

Apply it,

  $\begin{array}{c}\text{TSA}=2\left(lb+bh+hl\right)\\ =2\left(3a\right)\left(2a\right)+2\left(2a\right)a+2a\left(3a\right)\\ =12a^2+4a^2+6a^2\\ =22a^2\end{array}$

Thus, the total surface area of the solid is $22a^2$ .