Question

what is the volume of this cone? round your answer to the nearest hundredth. 18 mm 11 mm cubic millimeters submit

Explanation:

Step1: Recall Cone Volume Formula

The formula for the volume \( V \) of a cone is \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Identify Values

From the diagram, the radius \( r = 11 \) mm and the height \( h = 18 \) mm.

Step3: Substitute Values into Formula

Substitute \( r = 11 \) and \( h = 18 \) into the formula:
\( V = \frac{1}{3} \times \pi \times (11)^2 \times 18 \)
First, calculate \( (11)^2 = 121 \). Then, \( \frac{1}{3} \times 18 = 6 \). So, \( V = \pi \times 121 \times 6 \).
Calculate \( 121 \times 6 = 726 \). Thus, \( V = 726\pi \).

Step4: Compute Numerical Value

Using \( \pi \approx 3.14159 \), we get \( V \approx 726 \times 3.14159 \approx 2279.64 \) (rounded to the nearest hundredth).

Answer:

2279.64