Respuesta :
Answer:
0.0628cm/hr
Step-by-step explanation:
the snowball decreases in volume at a constant rate of 8 cubic cm per hour
Volume of a sphere = 4/3πr^3
Differentiate volume with respect to time(t)
dV/dt = 3(4/3πr^3)
= 4πr^2 . dr/dt
From the question, dV/dt = 8, r= 10
Substituting,
8 = 4π(10)^2 . dr/dt
8 = 400π . dr/dt
dr/dt = 8/400π
dr/dt =1/50π
dr/dt = 0.0628cm/hr
Answer:
0.006366 cm/h
Step-by-step explanation:
First we need to know that the volume of a sphere is calculated with the following formula:
V = (4/3)*pi*r^3
Where V is the volume and r is its radius.
Then, to find the rate of change, we need to derivate the equation with respect to the radius:
dV/dr = (4/3)*pi*(3r^2) = 4*pi*r^2
Then, we can write dV/dr as being (dV/dt)*(dt/dr), where dt is the change of time (variable t)
(dV/dt)*(dt/dr) = 4*pi*r^2
(dV/dt) = 4*pi*r^2*(dr/dt)
The rate of change of the volume is 8 cm3/h when the radius is 10, so using these values, we can find the rate of change of the radius (dr/dt):
8 = 4*pi*10^2*(dr/dt)
8 = 400*pi*(dr/dt)
dr/dt = 8/(400*pi)
dr/dt = 0.006366 cm/h
