Question

A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by v = x2h cm3. Find the rate at which the volume of the box is changing when the edge length of the base is 10 cm, the edge length of the base is increasing at a rate of 3 cm/min, the height of the box is 5 cm, and the height is decreasing at a rate of 1 cm/min.

Answer 1

Volume of square based box = (base) ^2 x height.

Original base 10 cm & height 5 cm

Volume of original box = 10^2 x 5

= 500 cu.m.

Change in base (increased) = 10+3=13 cm

Change in height (decreased) =5-1=4 cm

Volume of new box = base^2 x h

= 13^2 x 4 = 676 cu.m.

Change in volume = 676-500=176 cu.m.

Rate of change in volume =

(176/500) x 100= 35.2% [increase in volume]