Question

What is the maximum volume of a cone that would fit in the box with h=3cm, l=6cm, and w=3cm? how do i do this step by step

Answer 1

for d cone to fit in,it base must fit in with base area of box i.e the radius of cone is half width of box=1.5cm and it height must be 3cm V=1/3pi(1.5)^2*3

Answer 2

But why not lay the cone in sideways so that the base of the cone rests against the end of the box

So the base of the cone fits the 3 cm by 3 cm end and its height is 6 cm
radius = 1.5 cm
Volume = (1/3)π(1.5)^2 (6)
= 4.5π cm^3

(cosine's cone is only 2.25π cm^3)