Question

find the volume of the cone.
r = 6 cm
v = ? cm³
round to the nearest tenth.

Explanation:

Step1: Recall the formula for the volume of a cone

The formula for the volume \( V \) 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 problem, we have \( r = 6\space\text{cm} \) and \( h=9\space\text{cm} \).

Step3: Substitute the values into the formula

Substitute \( r = 6 \) and \( h = 9 \) into the formula:
\[

$$\begin{align*} V&=\frac{1}{3}\times\pi\times(6)^{2}\times9\\ &=\frac{1}{3}\times\pi\times36\times9\\ &=\pi\times12\times9\\ & = 108\pi \end{align*}$$

\]

Step4: Calculate the numerical value and round to the nearest tenth

We know that \( \pi\approx3.14159 \), so \( V = 108\times3.14159\approx339.3 \) (rounded to the nearest tenth).

Answer:

\( 339.3 \)