Q29. - Geometry

Question

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

Step-by-Step Solution

Answer

The volume is $50x^3$ and the surface area is $120x^2$.

Step 1. Given information.

A figure provided in the question,

Step 2. Determine values.

Firstly, for finding the volume of the solid, subtract the volume from the total volume.

$\begin{array}{c}v=(4x\times 3x)\left(5x\right)-(x\times 2x)\left(5x\right)\\ =60x^3-10x^3\text{ [multiply]}\\ =50x^3\text{ [subtract]}\end{array}$

 

Thus, the volume of the solid is .

Now find the surface area, add the all area.

$40x^2+30x^2+20x^2+10x^2+20x^2=120x^2$

 

Thus, the surface area is$120x^2$ .