6. + -M points LarCalc11 2.6.015. 0/10 submissions Used My Note All edges of a c

Question

6. + -M points LarCalc11 2.6.015. 0/10 submissions Used My Note All edges of a cube are expanding at a rate of 5 centimeters per second (a) How fast is the volume changing when each edge is 2 centimeter(s)? cm3/sec (b) How fast is the volume changing when each edge is 10 centimeters? cm /sec Need Help? Read ItTalk to Tuton 7. 1 points LarCalc11 2.6.017.MI. 0/10 Submissions Used My Note At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 2 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 2 feet high? (Hint: The formula for the volume of a cone is h.) ft/min Need Help? Read It Watch It Master It

Explanation / Answer

6 given cube has exapanding his edges at 5 cm/sec (=da/dt say)

now volume V = a3

dV/dt = 3a2 da/dt

i) when a=2 cm

dV/dt = 3 (22) *5

= 60 cm3/sec

ii) when a=10 cm

dV/dt = 3 (102) *5

= 1500 cm3/sec

7

given V = 1/3 pi r2h

dV/dt = 2 cubic feet/sec

h=2 ft

diameter = 3 *2

r = 3

now dV/dt = 1/3 pi r2 dh/dt

2 = 1/3 pi(32) dh/dt

dh/dt = 2/3pi ft/min

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