5)An ice block used for refridgeration is modeled as a cube of side s. The block

Question

5)An ice block used for refridgeration is modeled as a cube of side s. The block currently has volume 125,00 cubic cm and is melting at the rate of 1,000 cubic cm per hour. What is the current rate of change of the surface area S of the block with respect to time? Hint: S = 6s^2. An ice block used for refridgeration is modeled as a cube of side s. The block currently has volume 125,00 cubic cm and is melting at the rate of 1,000 cubic cm per hour. What is the current length s of each side of the cube? At what rate is s currently changing with respect to time t? Hint: V = s^3. An environmental study for a certain community indicates that there will be Q(p) = p^2 + 4p + 900 units of a harmful pollutant in the air when the popultion is p thousand people. If the population is currently p = 50,000 and is increasing at a rate of 1,500 per year, at what rate is the level of pollution increasing?

Explanation / Answer

the current length of the side = (12500)^1/3 = 50 cm We want ds/dt |s=50 We know dV/dt |s=50 = 1000 Find an equation that relates the s and V : V = s^3 V = s^3 ds/dt = 2/15 cm/hr Find an equation that relates the s and SA: SA = 6s^2 SA = 6s^2 SA/dt = 12(50)(2/15) = 4(10)(2) = 80

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