Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 25, 2024

Find the surface area of a cylinder given its radius $r$ and height $h$ .

STEP 1

Question: Which formula represents the surface area of a cylinder?
A) S = $\pi r^2 h$ B) S = $2\pi r h + \pi r^2$ C) S = $2\pi r h + 2\pi r^2$ D) S = $2\pi rh$
Answer: C)

STEP 2

Question: What is the first step to isolate the variable $h$ in the equation $S = 2\pi rh + 2\pi r^2$ ?
A) Add $2\pi r^2$ to both sides B) Subtract $2\pi r^2$ from both sides C) Divide both sides by $2\pi r$ D) Multiply both sides by $h$
Answer: B)

STEP 3

Question: After subtracting $2\pi r^2$ from both sides of the equation, what is the new equation?
A) $S + 2\pi r^2 = 2\pi rh$ B) $S = 2\pi rh - 2\pi r^2$ C) $S - 2\pi r^2 = 2\pi rh$ D) $S - 2\pi r^2 = 2\pi r$
Answer: C)

STEP 4

Question: How do you solve for $h$ after the subtraction step?
A) Multiply both sides by $2\pi r$ B) Add $2\pi r$ to both sides C) Divide both sides by $2\pi r^2$ D) Divide both sides by $2\pi r$
Answer: D)

STEP 5

Question: What is the final expression for $h$ in terms of $S$ and $r$ after simplifying the equation?
A) $h = S - 2\pi r^2$ B) $h = \frac{S}{2\pi r} - r$ C) $h = \frac{S - 2\pi r^2}{2\pi r}$ D) $h = \frac{2\pi r^2}{S - 2\pi r}$
Answer: C)

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