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Jack knows the surface area of a cylinder and its radius. He wants to find the cylinder's height. He needs to rewrite the formula [tex]A=2 \pi r(r+h)[/tex] to find the cylinder's height ([tex]h[/tex]) in terms of the cylinder's surface area ([tex]A[/tex]) and its radius ([tex]r[/tex]). Which is the correct formula?

A. [tex]h=r+\frac{A}{2 \pi r}[/tex]


Sagot :

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.