Question

question
find the volume of the figure. round to the hundredths when necessary.
(image of a cone with height 14 in and radius 9 in)

Explanation:

Step1: Recall the formula for the volume of a cone

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

Step2: Identify the values of \(r\) and \(h\)

From the figure, the radius \(r = 9\) inches and the height \(h=14\) inches.

Step3: Substitute the values into the formula

Substitute \(r = 9\) and \(h = 14\) into \(V=\frac{1}{3}\pi r^{2}h\).

$$
LATEXBLOCK0
$$

Step4: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(V = 378\times3.14159\approx1187.42\) cubic inches.

Answer:

\(1187.42\) cubic inches