Question

the length of diogonals of a cube is 6√5cm find suerfas area of a cube​

Answer 1

Step-by-step explanation:

$360 \: cm {}^{2}$

diagonal of cube (d) can be given as

$d = a \sqrt{3}$

where a is the edge of cube

$d = a \sqrt{3} \\ 6 \sqrt{5} = a \sqrt{3} \\ a = 6 \sqrt{ \frac{5}{3} } \: cm$

$surface \: area = 6 {a}^{2} \\ = 6 {(6 \sqrt{ \frac{5}{3} } )}^{2} = 6 \times 36 \times \frac{5}{3} \\ = 2 \times 36 \times 5 \\ = 360 \: {cm}^{2}$