Question
The sides of a cube are increasing in length at a constant rate of 5 cm/minute. At the moment that the surface area of the cube is 2400 cm^2, how fast is the VOLUME of the cube increasing?
Answers
oobleck
when A = 2400, s = 20
v = s^3
dv/dt = 3s^2 ds/dt = 3*400*5 = 6000 cm^3/s
or
v = (A/6)^(3/2)
dv/dt = 1/4 (A/6)^(1/2) dA/dt = 1/4 (A/6)^(1/2) * 12s ds/dt
= 1/4 * 20 * 12 * 20 * 5 = 6000 cm^3/s
v = s^3
dv/dt = 3s^2 ds/dt = 3*400*5 = 6000 cm^3/s
or
v = (A/6)^(3/2)
dv/dt = 1/4 (A/6)^(1/2) dA/dt = 1/4 (A/6)^(1/2) * 12s ds/dt
= 1/4 * 20 * 12 * 20 * 5 = 6000 cm^3/s