The volume of a cube is increasing at the rate of 1200 cm³/min at the instant its edges are 20 cm long. At what rate are the edges changing at that in

Efan Halliday

Efan Halliday

Answered question

2021-05-19

The volume of a cube is increasing at the rate of 1200 cm supmin at the instant its edges are 20 cm long. At what rate are the edges changing at that instant?

Answer & Explanation

aprovard

aprovard

Skilled2021-05-20Added 94 answers

The volume of a cube with edge length ee is given by:
V=e3
Differentiate with respect to t: dVdt=3e2(dedt)
Substitute dVdt=1200 cm3min and e=20 cm then solve for dedt: 1200=3(20)2(dedt)
1200=1200(dedt)
1=dedt
or
dedt=1cmmin

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