Given Information:
Radius of disk = r = 225 mm
Rate of change of radius = dr/dt = 0.04 mm/s
Required Information:
Rate of change of area = dA/dt = ?
Answer:
Rate of change of area = 56.54 mm²/s = 5.7x10⁻⁵ m²/s
Explanation:
Assuming that the disk is circular shaped then the area of disk is given by
A = πr²
Where r is the radius of the disk.
Differentiating the area with respect to time t
dA/dt = πr²
dA/dt = 2πrdr/dt
Where dr/dt is the rate of change of radius
dA/dt = 2π*225*(0.04)
dA/dt = 56.54 mm²/sec
or in standard units
(0.04 mm/s)/1000 = 4.0x10⁻⁵ m/s
(225 mm)/1000 = 0.225 m
dA/dt = 2π*0.225*(4.0x10⁻⁵)
dA/dt = 5.7x10⁻⁵ m²
Therefore, the area of the disk is changing at the rate of 5.7x10⁻⁵ m²/s
