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Question
The square on the diagonal of a cube has an area of 441 cm2. Find the length of the side and total surface area of the cube.
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Solution
Area of a Square = 441cm2
side2 = 441
side = `sqrt(441)`
∴ side = 21cm
∴ The length of the diagonals of the cube is 21cm.
Let 'a' be the side of the cube
Diagonal of a cube = `sqrt(3) xx "a"`
∴ 21 = `sqrt(3) xx "a"`
a = `(21)/sqrt(3)`
a = `(21)/sqrt(3) xx sqrt(3)/sqrt(3)`
(rationalising the denominator)
a = `(21sqrt(3))/(3)`
a = `7sqrt(3)"cm"`
Total surface area of a cube
= 6a2
= 6 x `(7sqrt(3))^2`
= 6 x 49 x 3
= 882cm2
∴ Side of the cube is `7sqrt(3)"cm"` and the total surface area of the cube is 882cm2.
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