Please provide explanations for 11 and 13

If the original 24 m edge length x of a cube decreases at the rate of 5 m/ min, when x = 3 m at what rate does the cube's a. surface area change? 9 b. volume change ? 12. A cube's surface area increases at the rate of 72 in2/ sec. At what rate is the cube's volume changing when the edge length is x = 3 in? .Volume The radius r and height h of a right circular cylinder are related to the cylinder's volume V by the formula V = mr h. a. How is dV/ dt related to dh/ dt if r is constant? b. How is dV / di related to dr / dt if h is constant? c. How is dV / dt related to dr / dt and dh / dt if neither r nor h is 20. constant? 14. Volume The radius r and height h of a right circular cone are related to the cone's volume V by the equation V = (1/3) Trzh. a. How is dV/ di related to dh / di if r is constant? b. How is dV / dt related to dr / dt if h is constant? c. How is dV / di related to dr / dt and dh / dt if neither r nor h is constant? 15. Changing voltage The voltage V (volts), current / (amperes), and resistance R (ohms) of an electric circuit like the one shown here are related by the equation V = IR. Suppose that V is increasing at the rate of 1 volt / sec while / is decreasing at the rate of 1/3 amp / sec. Let t denote time in seconds. 25 + h = 29. ~ 2.9 ft/ sec 23. JO 84 202 + 212 = (25 + h)2 62 a. What is the value of dV / dt? b. What is the value of dl / dt? = t . C. What equation relates dR / di to dV / dt and dl / dt? 21 29 ince we know dx/di, it remains only to find 25 + h at the instant d. Find the rate at which R is changing when V = 12 volts and (25 + h)2 = 841, 1 = 2 amps. Is R increasing, or decreasing? up IP 16. Electrical power The power P (watts) of an electric circuit is related to the circuit's resistance R (ohms) and current I (amperes) by the equation P = RI2. a. How are dP / dt, dR / dt, and dl / dt related if none of P, R, and I are constant? b. How is dR / di related to dl / dt if P is constant? Equation (2) now gives 17. Distance Let x and y be differentiable functions of t and let Equation (1), s = Vx2 + y be the distance between the points (x, 0) and so that (0, y) in the xy-plane. a. How is ds / dt related to dx / dt if y is constant