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