Question

what is the volume of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. image of a cone with 16 cm (diameter/radius) and 20 cm height cubic centimeters

Explanation:

Step1: Recall the volume formula for a cone

The volume \( V \) of a cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cone. From the diagram, the diameter of the base is \( 16 \) cm, so the radius \( r=\frac{16}{2} = 8 \) cm, and the height \( h = 20 \) cm. We are given \( \pi\approx3.14 \).

Step2: Substitute the values into the formula

First, calculate \( r^{2} \): \( r^{2}=8^{2}=64 \). Then, substitute \( r = 8 \), \( h=20 \), and \( \pi = 3.14 \) into the volume formula:
\[

$$\begin{align*} V&=\frac{1}{3}\times3.14\times64\times20\\ &=\frac{1}{3}\times3.14\times1280\\ &=\frac{4019.2}{3}\\ &\approx1339.73 \end{align*}$$

\]

Answer:

\( 1339.73 \)