Question

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

Explanation:

Step1: Recall volume formulas

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

Step2: Identify dimensions of cylinder

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

Step3: Identify dimensions of cone

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

Step4: Calculate 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:

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