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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Solution

Side length of the cube, a = 7 cm
Height of the cone, h = 7 cm
radius, r = 3 cm
Volume of the remaining solid = Volume of the cube − volume of the cone
V= $a^{3} - \frac{1}{3} π r^{2} h$
V= $7^{3} - \frac{1}{3} π (3^{2}) \times 7$
V= $343 - 66 = 277 c m^{3}$

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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.

Side length of the cube, a = 7 cmHeight of the cone, h = 7 cmradius, r = 3 cmVolume of the remaining solid = Volume of the cube − volume of the coneV=a3−13πr2hV=73−13π(32)×7V=343−66=277 cm3

Side length of the cube, a = 7 cm
Height of the cone, h = 7 cm
radius, r = 3 cm
Volume of the remaining solid = Volume of the cube − volume of the cone
V= $a^{3} - \frac{1}{3} π r^{2} h$
V= $7^{3} - \frac{1}{3} π (3^{2}) \times 7$
V= $343 - 66 = 277 c m^{3}$