Question

5
which formula can be used to find the volume, v, of the composite solid figure represented below?
image of a composite solid with a cylinder and a hemisphere
a. $v = \pi r^2 h + \frac{4}{3}\pi r^3$
b. $v = \pi r^2 h + \frac{2}{3}\pi r^3$
c. $v = \frac{1}{3}\pi r^2 h + \frac{4}{3}\pi r^3$
d. $v = \frac{1}{3}\pi r^2 h + \frac{2}{3}\pi r^3$

Explanation:

Step1: Identify the composite solids

The figure is a combination of a cylinder and a hemisphere.

Step2: Recall volume formulas

• Volume of a cylinder: $V_{\text{cylinder}} = \pi r^2 h$
• Volume of a sphere: $V_{\text{sphere}} = \frac{4}{3}\pi r^3$, so volume of a hemisphere (half of a sphere) is $V_{\text{hemisphere}} = \frac{1}{2} \times \frac{4}{3}\pi r^3 = \frac{2}{3}\pi r^3$

Step3: Combine the volumes

The total volume $V$ of the composite solid is the sum of the volume of the cylinder and the volume of the hemisphere: $V = \pi r^2 h + \frac{2}{3}\pi r^3$

Answer:

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