Question

If the volume of a cone is 168 pi inches and its altitude is 14 inches, what is the radius of the cone? A. 36 inches B. 12 inches C. 72 inches D. 6 inches

Answer 1

The radius of the cone is 6 inches, which i mentioned in option D, for the volume of a cone is 168$\pi$ inches and its altitude is 14 inches.

Step-by-step explanation:

The given is.

         Volume of the cone is 168$\pi$

         Altitude of the cone is 14 inches

Step:1

         Formula for Volume of cone is,

                     $V = \pi r^{2} \frac{h}{3}$....................................(1)

         Where,

                    V = 168 $\pi$ cubic inches

                      h = 14 inches

Step:2

          From the Eqn (1),

                     168$\pi$ = $\pi r^{2} \frac{14}{3}$                 (∵ Cancel  $\pi$ on both sides)

                        168 = $r^{2} \frac{14}{3}$

                  168 × 3 = $r^{2} 14$

                       504 = $r^{2} 14$

                           $r^{2}$ = 36

                             r = $\sqrt{36}$

                            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.