Respuesta :
The radius of the cone is 6 inches, which i mentioned in option D, for the volume of a cone is 168[tex]\pi[/tex] inches and its altitude is 14 inches.
Step-by-step explanation:
The given is.
Volume of the cone is 168[tex]\pi[/tex]
Altitude of the cone is 14 inches
Step:1
Formula for Volume of cone is,
[tex]V = \pi r^{2} \frac{h}{3}[/tex]....................................(1)
Where,
V = 168 [tex]\pi[/tex] cubic inches
h = 14 inches
Step:2
From the Eqn (1),
168[tex]\pi[/tex] = [tex]\pi r^{2} \frac{14}{3}[/tex] (∵ Cancel [tex]\pi[/tex] on both sides)
168 = [tex]r^{2} \frac{14}{3}[/tex]
168 × 3 = [tex]r^{2} 14[/tex]
504 = [tex]r^{2} 14[/tex]
[tex]r^{2}[/tex] = 36
r = [tex]\sqrt{36}[/tex]
r = 6 inches
Result:
Thus the radius of the cone is 6 inches, If the volume of a cone is 168 pi inches and its altitude is 14 inches.
