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/πr
c h = v/πr²
d h = v/πr
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:

Step1: Solve for \( h \) from \( V=\pi r^{2}h \)

Divide both sides by \( \pi r^{2} \).
$$h=\frac{V}{\pi r^{2}}$$

Step2: Substitute \( V = 36\pi\) and \( r = 3\)

$$h=\frac{36\pi}{\pi\times3^{2}}$$
Simplify \( \pi\) terms and calculate \( 3^{2}=9 \).
$$h=\frac{36\pi}{9\pi}$$
Cancel out \( \pi \) and divide \( 36\) by \( 9 \).
$$h = 4$$

Answer:

A. \( h=\frac{V}{\pi r^{2}} \)
\( h = 4\)