Question

The rate of change of volume with respect to R and the change in volume of the sphereas the radius is increased from 20.0 cm to 20.1 cm respectively are .......................... where R is the radius of the sphere and volume of a sphere is given by V = 4/3(pi)R^3.

(Assume that the rate does not appreciably change between R = 20.0 cm to R = 20.1 cm)

1) 4(pi)R^2 , 160(pi) cm^3
2) 4(pi)R^2 , 1600(pi) cm^3
3) 4(pi)R^2 , 16(pi) cm^3
4) none

HINT: Use differentiation

Answer 1

V= 4/3 pie r^3

dv/dr = 3× 4/3 pie r^2 = 4 pie r^2,

= 4 pie ( 20)^2 = 4 pie×400= 1600 pie

dv = 1600 pie × dr =1600pie( 20.1-20)

= 1600 × 0.1 × pie = 160 pie

A)