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  • From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

Answers (1)

Answer 277 cm3

Solution

            The figure formed when a conical cavity is cut out from a cube.

           

            Volume of cube =a^3

                        =(7)^3=343 cm^3

            The volume of the conical cavity

                         =\frac{1}{3}\pi r^2h

                        =\frac{1}{3}\times 3.14 \times (3)^2 \times 7     \left ( \because r=3cm ,h=7cm \right )

                        =21\times 3.14= 66cm^3

            The volume of remaining solid = volume of the cube – the volume of the conical cavity

                        =343-66= 277cm^3

           

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