Chapter 12.1, Problem 30WE

To determine

To find: the volume and the surface area of solid.

Answer to Problem 30WE

The volume is $72xy\text{+64}{x}^2$ and the surface area is $96x^{2}y$ .

Explanation of Solution

Given information:

A figure provided in the question,

  

Calculation: to find the surface area, first find the lateral area sand base area,

  $\begin{array}{l}\text{L}\text{.A}\text{.}=ph\\ \text{L}\text{.A}\text{.}=\left(8x+16x\right)3y\text{ [substitute]}\\ \text{L}\text{.A}\text{.}=72xy\text{ [simplify]}\\ \text{B}={\left(6x\right)}^2-4x^2\\ \text{B}=36x^2-4x^2\text{ [multiply]}\\ \text{B}=32x^2\text{ [subtract]}\end{array}$

Thus, the total surface area is.

  $\begin{array}{l}\text{T}\text{.A}\text{.}=\text{L}\text{.A}\text{.+2B}\\ \text{T}\text{.A}\text{.}=72xy\text{+64}{x}^2\text{ [simplify]}\end{array}$

Thus, the surface area is $72xy\text{+64}{x}^2$ .

To find the volume, multiply the base area by height,

  $\begin{array}{l}v=32x^2\left(3y\right)\\ v=96x^{2}y\text{ [multiply]}\end{array}$

Thus, the volume is $96x^{2}y$ .