Question

the radius of a cone can be found using the formula $r = sqrt{\frac{3v}{pi h}}$, where $v$ stands for the volume of the cone and $h$ stands for the height. if $r = 3$, $pi=3.14$, and $h = 6$, find the volume ($v$). round the answer to the nearest hundredths place.
37.68 cubic units
18.84 cubic units
56.52 cubic units
1.064.84 cubic units

Explanation:

Step1: Recall volume formula for cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$.

Step2: Substitute given values

We are given $r = 3$, $h=6$ and $\pi=3.14$. Substitute into the formula: $V=\frac{1}{3}\times3.14\times3^{2}\times6$.

Step3: Calculate exponent

First, calculate $3^{2}=9$. Then the expression becomes $V=\frac{1}{3}\times3.14\times9\times6$.

Step4: Perform multi - plications

$\frac{1}{3}\times9 = 3$, so $V=3.14\times3\times6$. Then $3\times6 = 18$, and $V=3.14\times18$.
$V = 56.52$ cubic units.

Answer:

56.52 cubic units