Mathematics
The square on the diagonal of a cube has an area of 192 cm2. Calculate :
(i) the side of the cube.
(ii) the total surface area of the cube.
Mensuration
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Answer
(i) Let a be the side of the cube.
The diagonal of the cube forms a square whose area is given:
Diagonal of cube = a
Since the square has an area of 192 cm2,
⇒ (a )2 = 192
⇒ a2 x 3 = 192
⇒ a2 =
⇒ a2 = 64
⇒ a =
⇒ a ≈ 8 cm
Hence, the side of the cube = 8 cm.
(ii) The total surface area of cube = 6a2
= 6 x 82
= 6 x 64
= 384 cm2
Hence, the total surface area of the cube = 384 cm2.
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