2) A computer graphic is being designed in which a cube is being zoomed in on. T

Question

2) A computer graphic is being designed in which a cube is being zoomed in on. The volume V, surface area S and length of the sides x are all varying with respect to time. Find the rate of change of the surface area when x=2 and the volume is increasing at a rate of 1 cubic unit per second

3) A hemispherical tank with a radius of 10m is filled from an input pipe at a rate of 3m^3/min (the volume if a cap if thickness h sliced from a sphere radius r is pi*h^2(3r-h)/3)
a) how fast is the water level rising when the water level is 5 m from the bottom of the tank?
b) what is the rate of change of the surface area of the water when the water is 5 m deep?

5) A conical tank with an upper radius of 10 m and a height of 8m drains into a cylindrical tank with a radius of 10m and a height of 10 m. if the water level in the conical tank drops at a rate of 0.5m/min, at what rate is the water level in the cylindrical tank rising when the water level in the conical tank is 4 m?

Explanation / Answer

rules are one question per post so I answered one question

2) V = x^3

dV/dt = 3 x^2 dx/dt

1 = 3*4 dx/dt

dx/dt = 1/12

SA = 6 * x^2

dSA/dt = 12 x dx/dt = 12*2*1/12 = 2

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