Question

Each side of a cube is increasing at the rate of 9cm/s . When the lenght of each side is 5 cm , find the rate of inscrease of its volume and total surface area .

Answer 1

(9+5)^3/(5^3)=rate of increase in volume

Answer 2

V = x^3 , where x is the length of the side

dV/dt = 3x^2 dx/dt
for the given data,
dV/dt = 3(5^2)(9)
= 675 cm^3/s

S = 6x^2, where S is the surface area
dS/dt = 12x dx/dt
= 12(5)(9)
= 540 cm^2/s