Answer:
The value of x would be 
Step-by-step explanation:
Given,
The dimension of the cardboard = 10 ft by 10 ft,
∵ After removing four equal squares of size x ( in ft ) from the corners,
The dimension of the resultant box would be,
Length = ( 10 - 2x ) ft,
Width = ( 10 - 2x ) ft,
Height = x ft,
The volume of box,

Differentiating with respect to x,

Again differentiating with respect to x,

For maxima or minima,



By quadratic formula,





For x = 5/3, V'' = negative,
While for x = 5, V'' = Positive,
Hence, the value of x would be 5/3 ft for maximising the volume.