Question

which formula can be used to find the volume, v, of the composite solid figure represented below?
a. $v = \pi r^2 h + \frac{4}{3}\pi r^3$
b. $v = \frac{1}{3}\pi r^2 h + \frac{4}{3}\pi r^3$
c. $v = \pi r^2 h + \frac{2}{3}\pi r^3$
d. $v = \frac{1}{3}\pi r^2 h + \frac{2}{3}\pi r^3$

Explanation:

Step1: Identify top solid (cylinder)

Volume of cylinder: $V_{cylinder}=\pi r^2 h$

Step2: Identify bottom solid (hemisphere)

Volume of hemisphere: $V_{hemisphere}=\frac{2}{3}\pi r^3$

Step3: Sum the two volumes

$V = V_{cylinder} + V_{hemisphere} = \pi r^2 h + \frac{2}{3}\pi r^3$

Answer:

C. $V = \pi r^2 h + \frac{2}{3}\pi r^3$