Question

Find the volume and the total surface area of each solid in terms of the given variables.

Short answer

The volume is$\left(72xy\text{+64}{x}^2\right)$ cube unit and the surface area is $96x^{2}y$square unit.

Step-by-step solution

Step 1. Given information.

A figure provided in the question,

Step 2. Determine the Surface Area.

To find the surface area, first find the lateral area sand base area,

$\begin{array}{c}\text{L.A.}=ph\\ =(8x+16x)3y\text{[substitute]}\\ =72xy\text{[simplify]}\end{array}$

And

$\begin{array}{c}\text{B}={\left(6x\right)}^2-4x^2\\ =36x^2-4x^2\text{[multiply]}\\ =32x^2\text{[subtract]}\end{array}$

Thus, the total surface area is.

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

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

Step 3. Determine the Volume.

Now find the volume, multiply the base area by height.

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

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