posted by Greg on .
The side of a square box is increasing at a rate of 4mm/s and its height is increasing at a rate of 2mm/s. How fast is the volume increasing when the side is 40mm and the height is 100mm.
Can someone just tell me what formula to use?
Don't always look for a formula.
Define your variables and "create" your own formula
let the square base have sides x by x
let the height be h
Volume = x^2 h ----- (from V = length x width x height)
using the product rule:
d(Volume)/dt = x^2 dh/dt + h(2x) dx/dt
we are given all those values
dV/dt = 40^2 (2) + 100(80)(4)