Question

A cylinder and a cone have the same volume. The cylinder has a radius of 2 inches and a hieght of 3 inches. The cone has a radius of 3 inches. What is the hieght of the cone?

Answer 1

The height of the cone is inches, if the cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.

Step-by-step explanation:

The given is,

          A cylinder and a cone have the same volume

          Cylinder has a radius 2 inches and height of 3 inches.

          Cone has a radius of 3 inches

Step:1

           For Cylinder'

           Formula to calculate the volume of cylinder is,

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

          where,

                      r - 2 inches

                      h - 3 inches

         From the equation (1)

                           = $\pi$ × $2^{2}$ × 3

                           = 37.70

                        V = 37.70 cubic inches

Step:2

         For cone,

         Formula to calculate the volume of cone is,

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

         From the statement,

                      cylinder and a cone have the same volume

                      $V_{cylinder}$ = $V_{cone}$

                          37.70 = $\pi$ × $3^{2}$ × $\frac{h}{3}$

                          37.70 = 9.42478 × h

Height of the cone, h = 4 inches

Result:

            Thus the height of the cone is 4 inches, if a cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.