Question

Find the volume of a cube whose diagonals is `sqrt(48)"cm"`.

Answer 1

Given that:
Diagonal of a cube = `sqrt(48)"cm"`
i.e., `sqrt(3) xx "l" = sqrt(48)`  ...[∵ Diagonal of cube = `sqrt(3) xx "l"]`

l = `sqrt(48)/sqrt(3)`

l = `sqrt(48/3)`

= `sqrt(16)`
= 4cm
∴ Side (l) = 4cm
Now,
Volume of cube
= l³
= l x l x l
= 4 x 4 x 4
= 16 x 4
= 64cm³
∴ Volume of Cube = 64cm³.