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Sand pouring from a container forms a conical pile whose height is equal to the diameter. If the height increases at a constant rate of 5 cm/s, find the rate of change in volume of sand when the pile is 10 cm high. constant rate of 4 cm3/sec molting at

Sand pouring from a container forms a conical pile whose height is equal to the diameter. If the height increases at a constant rate of 5 cm/s, find the rate of change in volume of sand when the pile is 10 cm high. constant rate of 4 cm3/sec molting at

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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31. no 5 do like example 8 solution

times the radius. Water is poured into a cylindrical tank whose height is when the radius is 3m ? times 3 2. Iron ore pouring from a chute forms a conical pile whose height is its radius. If the radius is 200 cm and the volume changes at a rate of 10000 cm's, find the rate of change of the radius. Sand is falling into a conical pile so that the radius of tha base of the pile is always e 3. to half of its height. If the sand is falling al the rate of 10 cm /sec, how fast is height the pile increasing when the pile is 5 cm deep? 4. Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always three times its height. Suppose the height of the pile increases at a rate of 2 cm/s when the height of the pile is 12 cm. At what rate is the sand leaving the bin at that instant? Sand pouring from a container forms a conical pile whose height is equal to the diameter. If the height increases at a constant rate of 5 cm/s, find the rate of change in volume of sand when the pile is 10 cm high. 6. An ice cube in the shape of a cube is melting at a constant rate of 4 cm/sec. Find the rate of change of the surface area of the cube when the volume is 8 cm. A block of ice in the shape of a cube is melting in such a way that the length of each of its edges is decreasing at the rate of 2 cm/hr. At what rate is its surface area decreasing at the time its volume is 64 cm ? Assume that the block of ice maintains its cubical shape.
Transcribed Image Text:times the radius. Water is poured into a cylindrical tank whose height is when the radius is 3m ? times 3 2. Iron ore pouring from a chute forms a conical pile whose height is its radius. If the radius is 200 cm and the volume changes at a rate of 10000 cm's, find the rate of change of the radius. Sand is falling into a conical pile so that the radius of tha base of the pile is always e 3. to half of its height. If the sand is falling al the rate of 10 cm /sec, how fast is height the pile increasing when the pile is 5 cm deep? 4. Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always three times its height. Suppose the height of the pile increases at a rate of 2 cm/s when the height of the pile is 12 cm. At what rate is the sand leaving the bin at that instant? Sand pouring from a container forms a conical pile whose height is equal to the diameter. If the height increases at a constant rate of 5 cm/s, find the rate of change in volume of sand when the pile is 10 cm high. 6. An ice cube in the shape of a cube is melting at a constant rate of 4 cm/sec. Find the rate of change of the surface area of the cube when the volume is 8 cm. A block of ice in the shape of a cube is melting in such a way that the length of each of its edges is decreasing at the rate of 2 cm/hr. At what rate is its surface area decreasing at the time its volume is 64 cm ? Assume that the block of ice maintains its cubical shape.
Example 8: A spherical balloon is being inflated at a rato of B cm's Cnd the rate of change of the surface area when the radius is 10 cm. Solution. dA AP 8. =7,r= 10 dt 4. dr A = 4xr dA 8ar %3D dr dA AP dv dA dt dA AP dr dV dt dr 1 8 x 8tr x 4ar %3D 8 x 81( 10 ) x 4m( 10ア 1.6 cm's %3D Alternative Solution: V = dt AP dt 4n( 10 dr dr %3! 50x dt A = 4nr dA dr 8ar dt 8n( 10) %3D 50m 1.6 cm's' %3D
Transcribed Image Text:Example 8: A spherical balloon is being inflated at a rato of B cm's Cnd the rate of change of the surface area when the radius is 10 cm. Solution. dA AP 8. =7,r= 10 dt 4. dr A = 4xr dA 8ar %3D dr dA AP dv dA dt dA AP dr dV dt dr 1 8 x 8tr x 4ar %3D 8 x 81( 10 ) x 4m( 10ア 1.6 cm's %3D Alternative Solution: V = dt AP dt 4n( 10 dr dr %3! 50x dt A = 4nr dA dr 8ar dt 8n( 10) %3D 50m 1.6 cm's' %3D
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