Answer:
The radius, in inches, of the base of the cone will be:
r = 6 inches
Hence, option B is correct.
Step-by-step explanation:
Given
The Volume of a right circular cone V = 24 π cubic inches
The height of the cone h = 2 inches
To determine
The radius of the base of the cone r = ?
Using the formula involving Volume m, height h, and radius r of a right circular cone.
[tex]V\:=\frac{1}{3}h\:\pi \:\:r^2\:[/tex]
substituting V = 24 π, h = 2 to find the radius r
[tex]\left(24\pi \right)=\frac{1}{3}\left(2\right)\:\pi \:r^2[/tex]
switch sides
[tex]\frac{1}{3}\left(2\right)\pi r^2=\left(24\pi \right)[/tex]
[tex]\frac{1}{3}2\pi r^2=24\pi[/tex]
simplify
[tex]2\pi r^2=72\pi[/tex]
Divide both sides by 2π
[tex]\frac{2\pi r^2}{2\pi }=\frac{72\pi }{2\pi }[/tex]
[tex]r^2=36[/tex]
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
[tex]r=\sqrt{36},\:r=-\sqrt{36}[/tex]
Thus,
[tex]r=6,\:r=-6[/tex]
As we know that the radius can not be negative.
Therefore, the radius, in inches, of the base of the cone will be:
Hence, option B is correct.
