29..answer no 7 do like example 3 solution 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. Example 3:The volume of water in a bowl is given by V= (36xx) where x cm is the depthof the water tf water is poured in at a rate of 10 cm's at what rate is the level risingwhen the depth is 8 cm ?Solution:dV= 10. = ?, x = 8dxdtn ( 36xx')V =dV* ( 72x - 3x )dx24x x%3DdVdxclxdtdtAP110 x24m X1.10 x24 (8)R(8)564cmsAlternative Solution:dV= 10, = ?, x = 8dxdt3*(36x - x)V.dV%3Ddl10 - (12(8) - 3(8y 1(384 )10 =dxdt64cms !

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The width of a rectangle increases at a rate of 2 cms. The length is five times its width. Find the rate at which the area is increasing when its width is5 cm.