Question

part a
the formula for the volume v of a cylinder is v = πr²h, where r is the radius of the base and h is the height of the cylinder. solve the formula for h.
choose the correct formula.
a h = v/πr²
b h = v/πr²
c h = vr²/π
d h = v/πr²
part b
find the height of a cylinder with a volume of 36π cm³ and a base with a radius of 3 cm
h = □ cm

Explanation:

Part A

Step1: Solve the formula for \( h \)

Given the volume formula of a cylinder \( V=\pi r^{2}h \).
To solve for \( h \), divide both sides of the equation by \( \pi r^{2} \).

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So the correct formula is \( h = \frac{V}{\pi r^{2}} \), which is option A.

Part B

Step1: Identify the values of \( V \) and \( r \)

We are given that \( V = 36\pi\space cm^{3} \) and \( r = 3\space cm \).

Step2: Substitute the values into the formula \( h=\frac{V}{\pi r^{2}} \)

Substitute \( V = 36\pi \) and \( r = 3 \) into the formula:

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Step3: Simplify the expression

Cancel out the \( \pi \) terms (\( \pi
eq0 \)) and then divide \( 36 \) by \( 9 \):

$$ h=\frac{36}{9}=4 $$

Answer:

• Part A: A. \( h=\frac{V}{\pi r^{2}} \)
• Part B: \( h = 4\space cm \)