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The square on the diagonal of a cube has an area of 1875 sq.cm. Calculate the total surface area of the cube.

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3750 {cm}^{2}

3050 {cm}^{2}

3000 {cm}^{2}

3700 {cm}^{2}

answer is A.

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Detailed Solution

Given,
Diagonals of cube square

= 1875 {cm}^{2}

If the side of cube = a cm
The diagonals length = side of square

(a \sqrt{3})^{2} = 1875

(\sqrt{3} a^{2}) = 1875

3 a^{2} = 1875

a^{2} = 625

a = 25 cm

Thus, the total surface area of the cube

TSA = 6 a^{2}

TSA

= 6 \times 25^{2}

TSA = 6 \times 625

TSA

3750 {cm}^{2}

Hence, option 1 is correct.

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