# Calculus

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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?

• Calculus -

Don't always look for a 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)
= ....

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