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 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 v(x) cubic centimetres, write the relation between v(x) and x as an equation.

iii) Calculate

Question

Philoid · Accepted Answer

(i) The side of the square = x

⇒ The dimensions of the box are

L = 7 – 2x

B = 5 – 2x

H = x

(ii) v(x) = L × B × H

⇒ v(x) = (7 - 2x) × (5 – 2x) × (x)

⇒ v(x) = (35 + 4x² -24x) × (x)

⇒ v(x) = 4x³ – 24x² + 35x – (1)

(iii) by (1)

⇒

Similarly,

v(1) = 4(1)³ – 24(1)² + 35(1)

⇒ v(1) = 15

And

⇒