Chapter 4.5, Problem 43WE

To determine

To find: the total surface area and the volume of given solid shown.

Answer to Problem 43WE

The total surface area of the solid = $48x^2$

And the volume of the solid = $20x^3$

Explanation of Solution

Given information:

Given figure

  

Calculation:

Solution:

Total surface area of the solid = sum of the areas of small rectangles.

  $\begin{array}{c}4x^2+2x^2+4x^2+4x^2+8x^2+6x^2+2\left(2x^2+8x^2\right)=28x^2+20x^2\\ =48x^2\end{array}$

Volume of the solid = sum of the volumes of the small cuboids forrmed

  $\begin{array}{c}\left(2x\right)\left(x\right)\left(2x\right)+\left(4x\right)\left(2x\right)\left(3x\right)=4x^3+16x^3\\ =20x^3\end{array}$

  $\therefore$ The total surface area of the solid = $48x^2$

And the volume of the solid = $20x^3$