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
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Answered by
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Volume of cube=(7)^3=343
Volume of cone=1/3*22/7*3*3*7=66
Remaining solid=343-66=277cm3
Volume of cone=1/3*22/7*3*3*7=66
Remaining solid=343-66=277cm3
Answered by
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Given that, side of a solid cube (a) = 7cm
Height of conical cavity i.e., cone, h = 7 cm
Since, the height of conical cavity and the side of cube is equal that means the conical cavity fit vertically in the cube.
Radius of conical cavity i.e., cone, r = 3 cm
⇒ Diameter = 2 x r = 2 x 3= 6 cm
Since, the diameter is less than the side of a cube that means the base of a conical cavity is
not fit in horizontal face of cube.
volume of cube =a^3
(7)^3=343
and volume of conical cavity
1/3πr^2h
1/3×22/7×3×3×7
66cm^3
therefore volume of remaining solid
volume of cube-volume of conical cavity
343-66=277cm^3
Hence, the required volume of solid is 277 cm³
Height of conical cavity i.e., cone, h = 7 cm
Since, the height of conical cavity and the side of cube is equal that means the conical cavity fit vertically in the cube.
Radius of conical cavity i.e., cone, r = 3 cm
⇒ Diameter = 2 x r = 2 x 3= 6 cm
Since, the diameter is less than the side of a cube that means the base of a conical cavity is
not fit in horizontal face of cube.
volume of cube =a^3
(7)^3=343
and volume of conical cavity
1/3πr^2h
1/3×22/7×3×3×7
66cm^3
therefore volume of remaining solid
volume of cube-volume of conical cavity
343-66=277cm^3
Hence, the required volume of solid is 277 cm³
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