1.

The lateral surface area of a cube is `324 cm^(2)`. Find its volume and the total surface area

Answer» Let each side of the cube be a cm
then, the lateral surface area of the cube `= (4a^(2)) cm^(2)`
`:. 4a^(2) = 324 rArr a^(2) = 81 rArr a = sqrt81 = 9`
Volume of the cube `= a^(3) cm^(3)`
`= (9 xx 9 xx 9) cm^(3) = 729 cm^(3)`
Total surface area of the cube `= (6a^(2))` sq units
`= (6 xx 9 xx 9) cm^(2) = 486 cm^(2)`


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