29..answer no 1 do like example 1 solution An emply container is filled with liquid. The height of the liquid in the container is x cm and itsvolume is V cm, where V= x (5+ 2x + Xx) If x increases at the rate ofExample 1:O 35 cm per second, find the rate of change in volume when x = 1 cmSolution:AP= ?, x = 1dx= 0,35.dtdtx (5 +2x + x)5x + 2x + xV =APdx5 + 4x + 3xdxdtdVAPdt%3Ddx0.35 x (5 + 4x + 3x )%3D0.35 x (5 + 4 + 3)%3D4.2 cm sAlternative Solution:dx= 0.35,dtdV= ?, x = 1dtV =x (5 + 2x + x )dVdt응- x(2 + 2x) + (5+ 2x + x)2(0.35) + 2(0.35 ) + 0.35 (5 + 2 + 1)4.2 cm s%3D An emply container is filled with liquid. The height of the liquid in the container is x cm1.and its volume is V cm, vwhere V =0.05 cm per second, find the rate of change in volume when x = 2 cm.2 nx ( 5x ). If x increases at the rate ofThe volume of liquid with depth x cm is given by V =12) + 24 cm.2.The liquid is added to the container at a constant rate of 0.5 cm'/sFind the rate of change of the depth of the liquid at the instant the depth is 5 cm.Water is poured into a container at a rate of 12 cm/sec. The volume of water in the3.3.(h + 8h ) where h is the height of water in the container.container is given by V =Find the rate of change at which the height of water is increasing when h = 8.3pShow that the area of an equilateral triangle with sides p cm is A =4If the side is changing at a rate of 0.05 cms, how fast is the area changing when theside is 5 cm.The area of a triangle is given by A =x². If the area is decreasing at the rate of5.4 cm?/min, find the rate at which x is changing at the instant when the area is 200 cm2.6. Two sides of a triangle are 4m and 5m in length and the angle between them isincreasing at a rate of 0.06 rad/second. Find the rate at which the area of the triangle isTCincreasing when the angle 0 is3(Hint:Area of triangleab sin C)The width of a rectangle increases at a rate of 2 cms. The length is five times itswidth. Find the rate at which the area is increasing when its width is 5 cm.

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An emply container is filled with liquid. The height of the liquid in the container is x cm and its volume is V cm, where V = 5 nx ( 5- x). If x increases at the rate of 0.05 cm per second, find the rate of change in volume when x = 2 cm.