Boyle\'s law states that if the temperature of a gas remains constant, then PV =

Question

Boyle's law states that if the temperature of a gas remains constant, then PV = c, where P = pressure, V = volume, and c is a constant. Given a quantity of gas at constant temperature, if V is decreasing at a rate of 14 in. 3/sec, at what rate is P increasing when P = 60 lb/in.2 and V = 40 in.3? The volume of a sphere is increasing at a rate of 9cm3/sec. Find the rate of change of its surface area when its volume is 256pi/3 cm3. (Do not round your answer.) The volume of a rectangular box with a square base remains constant at 1100 cm3 as the area of the base increase at a rate of 7 cm2/sec. Find the rate at which the height of the box is decreasing when each side of the base is 13 cm long.

Explanation / Answer

Question 1

PV = c

differentiating both side

P*(dV/dt) + V*(dP/dt) = 0

dP/dt = -P*dV/(V*dt)

dP/dt = 21

Question 2

volume = 4/3 * pi*r^3

256*pi*/3 = 4/3 *pi*r^3

r = 4

dv/dt = 4/3 *pi*r^2*dr/dt

dr/dt = 27/(64*pi)

therefore change of surface area

dA/dt = 4*pi*2*r*dr/dt

dA/dt = 32*pi*27/(64*pi)

dA/dt = 13.5

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