Find the volume, the lateral surface area, the total surface area and the diagonal of a cube, each of whose edges measures (a) 9m, (b) 6.5 cm. [Take ]

Given,


a) Edge of cube (a) = 9m


Volume of cube = a3 = 93 = 729 m3


Lateral surface area of cube = 4a2 = 4 × 92 = 4 × 81 = 324 m2


Total surface area of cube = 6a2 = 6 × 92 = 6 × 81 = 486 m2


Diagonal of cube = a = × 9 = 1.73 × 9 = 15.57 m


b) Edge of cube (a) = 6.5 cm


Volume of cube = a3 = 6.53 = 274.625 cm3


Lateral surface area of cube = 4a2 = 4 × 6.52 = 4 × 42.25 = 169 cm2


Total surface area of cube = 6a2 = 6 × 6.52 = 6 × 42.25 = 253.5 cm2


Diagonal of cube = a = × 6.5 = 1.73 × 6.5 = 11.245 cm


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