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- Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a lateral area. b total area. c volume.The velocity (in centimeters per second) of blood molecules flowing through a capillary of radius 0.008 cmis v = 6.4 × 10−8 − 0.001r2, where r is the distance from the molecule to the center of the capillary. Findthe rate of change of velocity with respect to r when r = 0.004 cm.The velocity (in centimeters per second) of blood molecules flowing through a capillary of radius 0.008 cm is v = 6.4 × 10−8 − 0.001r2, where r is the distance from the molecule to the center of the capillary. Find the rate of change of velocity with respect to r when r = 0.004 cm.
- Water is flowing into a vertical cylindrical tank or radius 2 meters at a rate of 8 cu. meters per minute. How fast is the water level rising?Find the rate of change of the area of a square with respect to the length z of a diagonal. What is the rate when z=4?A cylinder has a height equal to its radius. Find the rate of change of volume V with respect to radius. dv/dr = ??
- Water is flowing into a conical vessel 9 m deep and having a radius of 3 m across the top. If the rate which the water rises is 2 m/sec, how fast is the water flowing into the conical vessel when the water is 4 m deep?A ladder 35 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 3 feet per second. 1. How fast is the top of the ladder moving down the wall when its base is 7 feet from the wall? 2. Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall. 3. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall.A conical vase is being filled with water at a rate of 10 cu. cm/s. The vase is 30 cm high and has a radius of 4 cm at the top. Find the rate at which the water level is rising when the depth of the water is 20 cm.
- A right circular cone has a fixed height of 7 units. Find the rate of change of its volume v with respect to the radius r of its base.The base of an oblique prism is an equilateral triangle of edge 20 cm. The lateral edges of the prism are 25 cm long and are inclined at a slope √3 horizontal to the plane of the base. Compute the volume of the prism. Hint: slope = tan(angle of inclination)The area between two infinite flat parallel sheets which are placed 10mm away from each other is occupied with a fluid having dynamic viscosity 0.5Pa.s. Through this distance between the sheets a plate with small thickness and cross sectional area 0.1m2 is being pulled. Considering the plate is at 4mm distance from one of the sheets and the velocity distribution is linear determine the amount of force which is needed to pull the plate.