applications of calculus - help needed urgently (1 Viewer)

[Petinga]

1 a spherical ballon is being inflated with air at a rate of 100cm^3/min. At what rate is the radius of the sphere increasing when the radius is 5cm?

2. Water is being poured into an inverted conical vessel whose apex aqngle is 90 degees and at a constant rate of 3cm^3/second. At what rate is the water level rising when the depth is pie cm?

 

[richz]

1) dV/dt = 100cm^3/min

dr/dt = dV/dt * dr/dV

V=4/3.pi.r^3

dV/dr = 4.pi.r^2 r= 5

dV/dr= 100.pi

dr/dV = 1/(100.pi)

so dr/dt = 100 *1/(100.pi)
= 1/pi


2) similar to 1, the volume of a cone is (1/3).pi.r^2.h

 

[rama_v]

1 a spherical ballon is being inflated with air at a rate of 100cm^3/min. At what rate is the radius of the sphere increasing when the radius is 5cm?

2. Water is being poured into an inverted conical vessel whose apex aqngle is 90 degees and at a constant rate of 3cm^3/second. At what rate is the water level rising when the depth is pie cm?

V = (1/3)pi r²h
dV/dt = 3cm³/s
dh/dt = dV/dt . dh/dV

but r = h since the angle is 45 degrees (90/2)
so V = (1/3)pi h³
dV/dh = pih²
.: dh/dt = 3 . 1/pi(pi²)
= 3/pi³