1) A parabolic shaped vessel is such hthat when it contains liquid to a depth of ycm, the volume of the liquid is 0.75y^4 cm^3. liquid is poured into the vessel at the rate of 40cm^3 per minute, at what rate is the level of the lqiuid rising when the depth of the liquid is 6cm.
2)a cone with base radius r, vertical height h and slant edge length l has curved surface area S= πrl and volume =1/3πr^2h
a)if a cone has vertical height x and its base radius is 0.75 of its vertical height, show that S= (15πx^2)/16 and v=(3πx^3)/16
A container is filled to overflowing with water. a solid cone with its axis vertical and its vertex pointing downwards is being lowered into the wtaer at a constant rate. the base radius of the cone is 0.75 of its vertical height. when the vertex of the cone is 2m under water (with the cone not fully submerged), the surface are of the cone is being covered with water at a rate of 0.5m^2/s.
b) show that teh cone is being lowered into the water at a rate of 2/15πm/s
c) find the rate at which the wtaer is overflowing the container when the vertex of the cone is 2m under water.
PLEASE PROVIDE FULL WORKED SOLUTIONS THANK YOU
2)a cone with base radius r, vertical height h and slant edge length l has curved surface area S= πrl and volume =1/3πr^2h
a)if a cone has vertical height x and its base radius is 0.75 of its vertical height, show that S= (15πx^2)/16 and v=(3πx^3)/16
A container is filled to overflowing with water. a solid cone with its axis vertical and its vertex pointing downwards is being lowered into the wtaer at a constant rate. the base radius of the cone is 0.75 of its vertical height. when the vertex of the cone is 2m under water (with the cone not fully submerged), the surface are of the cone is being covered with water at a rate of 0.5m^2/s.
b) show that teh cone is being lowered into the water at a rate of 2/15πm/s
c) find the rate at which the wtaer is overflowing the container when the vertex of the cone is 2m under water.
PLEASE PROVIDE FULL WORKED SOLUTIONS THANK YOU
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