The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.8 in/s. At what rate is the volume of the cone changing when the radius is 138 in. and the height is 143 in.?

34191.7πin³/sec

Step-by-step explanation:

Volume of circular come = 1/3pi x r² x h

When we differentiate this formula we have

dv/dt = 1/3π[r²dh/dt + 2rhdr/dt]

We have the following information

r = 138

H = 143 inch

dr/dt = 1.4

dh/dt = -2.8

When we plug into the formula

1/3π[130² x -2.8 + 2x138x143x1.4]

= 34191.7πin³/sec

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: