find the volume of the composite solid, which has a circular base. note that the figure is not to scale…

Explanation:

Step1: Identify base radius

The circular base has a diameter of 12, so radius $r = \frac{12}{2} = 6$.

Step2: Calculate volume of cone

Use cone volume formula $V_{cone} = \frac{1}{3}\pi r^2 h$, where $h=16$. $V_{cone} = \frac{1}{3}\pi (6)^2 (16) = \frac{1}{3}\pi \times 36 \times 16 = 192\pi$

Step3: Calculate volume of cylinder

Use cylinder volume formula $V_{cylinder} = \pi r^2 h$, where $h=5$. $V_{cylinder} = \pi (6)^2 (5) = \pi \times 36 \times 5 = 180\pi$

Step4: Sum volumes for total

Add the two volumes together. $V_{total} = 192\pi + 180\pi = 372\pi$ Calculate numerical value: $372 \times 3.1416 \approx 1168.74$

Answer:

1168.74