V = 441 cm³ (rounding up to the nearest whole)
1) Since the Volume of the Cone is given by:
[tex]V=\frac{1}{3}\pi r^2\text{h}[/tex]2) The measure of the height is 9cm and the area of the base is 147.
Since the area of a cone is a Circle. Then we can find the radius, applying the Circle Area formula to that:
[tex]\begin{gathered} A_{\text{circle}}=\pi\text{ r²} \\ 147=\pir^2 \\ \frac{147}{\pi}=\frac{\pi r^2}{\pi} \\ r^2=46.791 \\ \sqrt[]{r^2}=\sqrt[]{46.791} \\ r=6.84 \end{gathered}[/tex]3) Now that we have that radius we can plug that into the Volume of The cone
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2\text{h} \\ V=\frac{1}{3}\pi(6.84)^2\cdot9 \\ V\approx440.94cm^3 \end{gathered}[/tex]Then the Volume of the cone is approximately 440. 94 cm³ or rounding off to the nearest whole number 441 cm³
