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.?
1 answer:
Answer:
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
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