Question

From the four corners of a rectangle, small squares are cut off and the sides are folded up to make a box, as shown below:

i. Taking a side of the square as x centimetres, write the dimensions of the box in terms of x.

ii. Taking the volume of the box as vfojcubic centimetres, write the relation between v(x) and x as an equation.

iii. Calculate V(1/2), V(1), V(\(1\frac{1}{2}\))

Answer 1

If 1cm is the length of the small squares they are cut off, then the length of the maked box by folding it up = 7 – 1 – 1 = 5 cm Width = 5 – 1 – 1 = 3 cm, Height = 1 cm If 2 cm is the length of the small squares that are cut off, then the length of the maked box by folding it up = 7 – 2 – 2 = 3 cm Width = 5 – 2 – 2 = 1 cm, Height = 2cm 

i. If x cm is the length of the small squares that are cut off, then the length of the maked box by folding it up = 7 – x – x = (7 – 2x) cm 

Width = 5 – x – x = (5 – 2x) cm 

Height = x cm

ii. If volume of the box be v(x), then v(x) = Length × Width × Height v(x) = (7 – 2x) (5 – 2x)x cm³

v (1) = (7 – 2 × 1) (5 – 2 × 1) 1 = (7 – 2) (5 – 2) × 1 = 5 × 3 × 1 = 15