Question

Consider this composite figure made of a cone and a cylinder. A cone has a height of 8 centimeters and radius of 3 centimeters. A cylinder has a height of 7 centimeters and radius of 3 centimeters. What is the volume of the cone?

Answer 1

The volume of cone is 75.4 cubic centimeters and the volume of cylinder is 197.92 cubic centimeters. The volume of composite figure is 273.32 cubic centimeters.

Step-by-step explanation:

The given is,

                Composite figure made of a cone and a cylinder.

                A cone has a height of 8 centimeters and radius of 3 centimeters.

                A cylinder has a height of 7 centimeters and radius of 3 centimeters.

Step:1

              Volume of composite figure = Volume of Cone +

                                                                 Volume of cylinder............(1)

Step:2

            Formula for volume of cone,

                   $Volume of cone, V_{cone} = \pi r^{2} \frac{h}{3}$....................(2)

           Where, r - Radius of cone

                       h - Height of cone

           From the given,

                            r = 3 centimeters

                           h = 8 centimeters

           Equation (2) becomes,

                                                   $= \pi (3^{2} )(\frac{8}{3})$

                                                   $=\pi (9)(2.667)$

                                                   = (3.14 × 9 × 2.667)           (∵ $\pi$ = 3.1415)

                                                   = 75.4

                $Volume of cone, V_{cone}$ = 75.4 cubic centimeters

Step:3

           Formula for volume of cylinder,

                   $Volume of cone, V_{cone} = \pi r^{2} h$....................(2)

           Where, r - Radius of cylinder

                       h - Height of cylinder

           From the given,

                            r = 3 centimeters

                           h = 7 centimeters

           Equation (2) becomes,

                                                   $= \pi (3^{2} )(7)$

                                                   $=\pi (9)(7)$

                                                   = (3.14 × 9 × 7)           (∵ $\pi$ = 3.1415)

                                                   = 197.92

                $Volume of cylinder, V_{cylinder}$ = 197.92 cubic centimeters

Step:4

         Equation (1) becomes,

            Volume of composite figure = 75.4 + 197.92

                                                            = 273.32 cubic centimeters    

Result:

           The volume of cone is 75.4 cubic centimeters and the volume of cylinder is 197.92 cubic centimeters. The volume of composite figure is 273.32 cubic centimeters.