Sure! Let's start with the given formula for the surface area of a cylinder, which is:
[tex]\[ A = 2 \pi r (r + h) \][/tex]
We need to solve for [tex]\( h \)[/tex] in terms of the surface area [tex]\( A \)[/tex] and the radius [tex]\( r \)[/tex].
1. Start by dividing both sides by [tex]\( 2 \pi r \)[/tex] to isolate the term containing [tex]\( h \)[/tex]:
[tex]\[ \frac{A}{2 \pi r} = r + h \][/tex]
2. Now, subtract [tex]\( r \)[/tex] from both sides to get [tex]\( h \)[/tex] by itself:
[tex]\[ \frac{A}{2 \pi r} - r = h \][/tex]
Thus, the formula for the height [tex]\( h \)[/tex] of the cylinder in terms of its surface area [tex]\( A \)[/tex] and its radius [tex]\( r \)[/tex] is:
[tex]\[ h = \frac{A}{2 \pi r} - r \][/tex]
So, the correct formula is:
[tex]\[ h = \frac{A}{2 \pi r} - r \][/tex]
This formula allows Jack to find the height of the cylinder when he knows the surface area [tex]\( A \)[/tex] and the radius [tex]\( r \)[/tex] of the cylinder.
