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The following formula gives the surface area
S of a right cylinder, where
r is the radius of the base and
h is the height:

S=2pi r(r+h)
Rearrange the formula to highlight the height.

h=◻

The following formula gives the surface area $S$ of a right cylinder, where $r$ is the radius of the base and $h$ is the height: $\newline$ $S=2 \pi r(r+h)$ $\newline$ Rearrange the formula to highlight the height. $\newline$ $h=\square$

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Write equations of cosine functions using properties

Full solution

Q. The following formula gives the surface area

S

of a right cylinder, where

r

is the radius of the base and

h

is the height:

\newline

S=2 \pi r(r+h)

\newline

Rearrange the formula to highlight the height.

\newline

h=\square

Divide by $2\pi r$ : The formula for the surface area of a right cylinder is given by $S = 2\pi r(r + h)$ . To isolate $h$ , we first need to divide both sides of the equation by $2\pi r$ .
Cancel out $2\pi r$ : Dividing both sides by $2\pi r$ gives us $\frac{S}{2\pi r} = \frac{2\pi r(r + h)}{2\pi r}$ . The $2\pi r$ on the right side cancels out, leaving us with $\frac{S}{2\pi r} = r + h$ .
Subtract $r$ : Next, we subtract $r$ from both sides to isolate $h$ . This gives us $\left(\frac{S}{2\pi r}\right) - r = h$ .
Isolate $h$ : The equation with $h$ isolated is $h = \frac{S}{2\pi r} - r$ . This is the rearranged formula highlighting the height $h$ .

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