Question

which expression represents the volume, in cubic units, of the composite figure? o $pi(5^{2})(13)-\frac{1}{3}pi(5^{2})(12)$ o $pi(5^{2})(13)-\frac{1}{3}pi(5^{2})(25)$ o $pi(5^{2})(13)+\frac{1}{3}pi(5^{2})(12)$ o $pi(5^{2})(13)+\frac{1}{3}pi(5^{2})(25)$

Explanation:

Step1: Recall volume formulas

Volume of a cylinder $V_{cylinder}=\pi r^{2}h$ and volume of a cone $V_{cone}=\frac{1}{3}\pi r^{2}h$.

Step2: Identify dimensions for cylinder

For the cylinder in the composite - figure, radius $r = 5$ and height $h=13$. So, $V_{cylinder}=\pi(5^{2})(13)$.

Step3: Identify dimensions for cone

The total height of the figure is 25 and the height of the cylinder is 13, so the height of the cone $h = 25 - 13=12$, and radius $r = 5$. So, $V_{cone}=\frac{1}{3}\pi(5^{2})(12)$.

Step4: Find volume of composite - figure

The volume of the composite figure is the sum of the volume of the cylinder and the volume of the cone. So, $V = V_{cylinder}+V_{cone}=\pi(5^{2})(13)+\frac{1}{3}\pi(5^{2})(12)$.

Answer:

$\pi(5^{2})(13)+\frac{1}{3}\pi(5^{2})(12)$