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

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

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

Answer

Explanation:

Step1: Recall volume formulas

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

Step2: Identify dimensions

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

Step3: Find volume of composite - figure

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

Answer:

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