Question

All edges of a cube are expanding at a rate of 6 centimeters per second. (a) How fast is the volume changing when each edge is 5 centimeter(s)

Answer 1

Answer:

(a).The volume of cube is changing at the rate $450 cm^3/s$

Step-by-step explanation:

Let x be the side of cube

$\frac{dx}{dt}=6 cm/s$

We have to find the rate at which  volume of cube changing when edge is 5 cm.

We know that

Volume of cube, V=$x^3$

Differentiate w.r.t t

$\frac{dV}{dt}=3x^2\frac{dx}{dt}$

Substitute the values

$\frac{dV}{dt}=3(5)^2\times 6$

$\frac{dV}{dt}=450 cm^3/s$

Hence, the volume of cube is changing at the rate $450 cm^3/s$