find the volume of a right circular cone that has a height of 17 m and a base with a circumference of 6.3 m…

Explanation:

Step1: Find the radius from the circumference

The formula for the circumference of a circle is $C = 2\pi r$. Given $C=6.3$ m, we can solve for $r$: $r=\frac{C}{2\pi}=\frac{6.3}{2\pi}$ m.

Step2: Calculate the volume of the cone

The formula for the volume of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $h = 17$ m and $r=\frac{6.3}{2\pi}$ into the formula: [ \begin{align*} V&=\frac{1}{3}\pi(\frac{6.3}{2\pi})^{2}\times17\ &=\frac{1}{3}\pi\times\frac{6.3^{2}}{4\pi^{2}}\times17\ &=\frac{1}{3}\times\frac{6.3^{2}\times17}{4\pi}\ &=\frac{1}{3}\times\frac{39.69\times17}{4\pi}\ &=\frac{1}{3}\times\frac{674.73}{4\pi}\ &=\frac{674.73}{12\pi}\approx 17.9 \end{align*} ]

Answer:

$17.9$ m³