Question

the surface area of a cube is 800 cm .find the length of its diagonal.​

Answer 1

Answer:

given TSA of cube = 800 cm³

to find the diagonal of the cube

TSA of a cube = 6 a²

=> 6a² = 800

=> a² = 800/6

=> a² = 400/3

=> a = 20/√3 cm

diagonal of a cube = √(a²+a²+a²)

= √3a² = a√3

therefore diagonal = 20/√3 × √3/1

= 20 cm

Answer 2

Answer:

d=20

Step-by-step explanation:

total surface area of a cube is

$6{a}^{2} = 800 \\ a = \sqrt{ \frac{800}{6} } = \sqrt{ \frac{400}{3} } = \frac{20}{ \sqrt{3} } \\ the \: diagonal \: of \: a \: cube \: is \: \sqrt{3} a \\ = \sqrt{3} \times \frac{20}{ \sqrt{3} } = 20$