Question

Find the volume of the figure: a prism of volume 15 with a pyramid of the same height cut out.

Answer 1

The volume of the figure is 10 cubic units, if a prism of volume 15 with a pyramid of the same height cut out.

Step-by-step explanation:

The given is,

                A prism of volume 15

                A pyramid of the same height cut out

               For the above question diagram is missing, so i attach the diagram.

Step:1

            Ref the attachment,

                   Volume of figure = Volume of Prism - Volume of Pyramid....(1)

Step:2

           From the given diagram,

           Formula for volume of prism,

                                     $V_{prism} = whl$......................(2)

          Where, w - Width of the prism

                        h - Height of prism

                         l - Length of prism

        From the given,

        Volume, V = 15 cubic units

                         l = a

                       w = b

                        h = c

         Equation (1) becomes,

                                    15 = abc

                                      c = $\frac{15}{ab}$

Step:3

          Volume of pyramid, $V = \frac{whl}{3}$..........................(2)

          where,

                      w - Width of pyramid

                       h - Height of pyramid

                        l - Length of pyramid                              

           From the given,

                      l = a

                    w = b

                     h = c

         From the volume of prism, h = c = $\frac{15}{ab}$

         Equation (2) becomes,

                                           $V_{pyramid} = (\frac{ab}{3} )(\frac{15}{ab } )$

                                                         = 5

                                          $V_{pyramid} = 5$ cubic units

Step:4

        Equation (1) becomes,

                         Volume of figure = 15 - 5

                                                       = 10 cubic units

Result:

        The volume of the figure is 10 cubic units, if a prism of volume 15 with a pyramid of the same height cut out.