Explain for me if the radius of a circle is

If the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic meters

Five circles are placed in a rectangle as shown. If the length of the shorter side of the rectangle is 1, find the length of the other side.

Three pipes, each of radius length 4 in., are stacked as shown. What is the exact height of the stack?

Two circles, whose radii are 12 inches and 16 inches respectively, intersect. The angle between the tangents at either of the points of intersection is ${\displaystyle {20}^{\circ },{30}^{\prime }}$. Find the distance between the centers of the circle.

Draw a graph for the original figure and its dilated image. Check whether the dilation is a similarity transformation or not.
Given:
The given vertices are
M(1,4), P(2,2), Q(5,5), S(-3,6),T(0,0),U(9,9)

I have encountered that in some cases maximization of a function had been substituted with a maximization of its monotone transformation.

For example, finding the min or max of $f(x,y)=((x-1{)}^2+(y-2{)}^2{)}^{1/2}$ is the same as finding the min / max of $(x^2+y^2)$ and then take the square root of the answer. So, my questions are:
1) Is it true for any monotone transformation $g$?
2) Is the same principle allow us to maximize /minimize $\log g(x)$ instead of $g(x)$ itself?

Circles ${\displaystyle x^2+y^2-2x-2y-2=0}$ and ${\displaystyle x^2-y^2-8x-10y+32=0}$