Question

a cube is expanding and its volume is increasing at the rate 96 cubic centimetres/second when the side is 4 cm.Find the rate at which the:

a.side is increasing when the side is 4 cm

b.surface area is increasing when the side is 4cm

V= x^3 A= 6x^2

Answer 1

dV/dt = 3x^2 dx/dt
96 = 3(4^2)dx/dt
dx/dt = 96/48 = 2 cm/second

A = 6x^2
dA/dt = 12x dx/dt
dA/dt = 12(4)(2) = 96 cm^2/sec

Answer 2

A spherical balloon is being inflated and its radius is changing at the rate of 2m/minute. When the radius is 4m, find the rate at which the:

(a).volume is increasing

V= 3/4 pie r^2

(b). surface area is increasing

A = 4 pie r^2