The radius of a right circular cone is increasing at a rate of 1.6 in/s while its height is decreasing at a rate of 2.2 in/s. At
what rate is the volume of the cone changing when the radius is 135 in. and the height is 135 in.
1 answer:
Answer:
Step-by-step explanation:
let radius=r
height=h
dr/dt=1.6 in/s
dh/dt=-2.2 in/s
volume v=1/3 πr²h
dv/dt=1/3 π[h*2r×dr/dt+r²×dh/dt]
when r=135 in
h=135 in
dv/dt=1/3 π[2×135×135×1.6+135²×(-2.2)]
=1/3 π[135²(3.2-2.2)]
=1/3π135²×1
=6075 π in³/s
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