Question

The radius of a sphere is increasing at a rate of 0.50., point, 5 centimeters per minute. At a certain instant, the radius is 17 centimeters. What is the rate of change of the volume of the sphere at that instant (in cubic centimeters per minute)

Answer 1

Answer: 578π

Explanation:

dr/dt = 0.5

radius = 17

The volume of a sphere with radius is 4/3πr²

dv/dt = 4πr² (dr/dt)

dv/dt = 4π (17)²(0.5)

dv/dt = 578π

Answer 2

dV/dt = 1814,92 cm³/min

Explanation:

Volume of the sphere is :

V(s) = (4/3)*π*x³ (1) x is radius of the sphere

Differentiating in relation to time of equation (1)

dV/dt =(4/3)*π*3*x²*dx/dt

Now we know dx/dt = 0, 5 cm/min

And we have to find dV/dt when radius is 17 cm

dV/dt = 4*π*x²*0,5

dV/dt = 12,56*(17)²*0,5

dV/dt = 12,56*289*0,5

dV/dt = 1814,92 cm³/min