Question

a sphere and a right cylinder have the same radius and volume. find the radius r in terms of the height h of the cylinder. r =

Explanation:

Step1: Write volume formulas

Volume of sphere \( V_s=\frac{4}{3}\pi r^{3} \), volume of cylinder \( V_c = \pi r^{2}h \).

Step2: Set volumes equal

Since \( V_s = V_c \), we have \( \frac{4}{3}\pi r^{3}=\pi r^{2}h \).

Step3: Solve for \( r \)

Divide both sides by \( \pi r^{2} \) (assuming \( r
eq0 \)). We get \( r=\frac{3}{4}h \).

Answer:

\( r = \frac{3}{4}h \)