S=2πr^2+2πrh
Solve for h

Answers

Answer 1

Answer:

h = [S / (2πr)] - r

Further explanation

It is a case about two-variable linear equations and we have to solve the equation to get the variable h.

Our main plan is to isolate the variable h alone at the end of the process on one side of the equation until the variable will be equal to the value on the opposite side.

$\boxed{S = 2 \pi r^2 + 2 \pi rh}$

We can set it to be like this, i.e., just swapping positions on both sides but not changing the signs.

$\boxed{2 \pi r^2 + 2 \pi rh = S}$

We subtract both sides with $\boxed{2 \pi r^2}$ .

$\boxed{2 \pi r^2 + 2 \pi rh - 2 \pi r^2 = S - 2 \pi r^2}$

$\boxed{2 \pi rh = S - 2 \pi r^2}$

We divide both sides with $\boxed{2 \pi r}$

$\boxed{(2 \pi rh)/(2 \pi r) = (S - 2 \pi r^2)/(2 \pi r)}$

$\boxed{h = (S)/(2 \pi r) - (2 \pi r^2)/(2 \pi r)}$

We get the results as follows: $\boxed{\boxed{h= (S)/(2 \pi r) - r}}$

- - - - - - -

Let's check again from the beginning.

For example, r = 2 and h = 3, then we first calculate the value of S by using the initial equation.

$\boxed{S=2 \pi (2)^2 + 2 \pi (2)(3)}$

$\boxed{S = 8 \pi + 12 \pi }$

$\boxed{\boxed{S= 20 \pi}}$

Then, we substitute the results of S (with r = 2) into the new equation that we have compiled with h as the subject.

$\boxed{h =(20 \pi)/(2 \pi (2)) - 2}$

$\boxed{h = 5 - 2}$

We get the value h = 3 and it means that the equation has been proven.

Notes:

The formula that we discussed above is a formula for calculating the surface area of a closed cylinder.

$\boxed{S = 2 \pi r^2 + 2 \pi rh}$

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Keywords: S=2πr^2+2πrh, solve for h, subtract, divide, subject, to isolate the variable h alone, two-variable linear equations

Answer 2

Answer:

Final answer:

To solve for 'h' in the equation S = 2πr^2 + 2πrh, subtract 2πr^2 from both sides, divide by 2πr, simplifying the right side of the equation.

Explanation:

To solve for h in the equation S = 2πr^2 + 2πrh:

Start by subtracting 2πr^2 from both sides of the equation to isolate the term containing h.
This gives us 2πrh = S - 2πr^2.
To solve for h, divide both sides of the equation by 2πr.
The final step is to simplify the right side of the equation, giving us h = (S - 2πr^2) / (2πr).

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S=2πr^2+2πrhSolve for h

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Further explanation

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Explanation:

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S=2πr^2+2πrh
Solve for h