The square on the diagonal of a cube has an area of 192cm². Calculate (i) the side of the cube in cm (ii) the total surface area of the cube in cm²
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Answer:
side of cube = 8 cm
total surface area = 384 cm²
Step-by-step explanation:
diagonal of cube = D
side of cube = S
D = S√3 (equation for diagonal of cube)
D² = 192cm²
∴192 = (S√3)²
192 = S² × 3
S² = 64
S = √64 = 8
total surface area = 6S²
total surface area = 6 × 8² = 6 × 64
total surface area = 384cm²
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