Question

the volume of a cube is increasing at a rate of 10cm³/min. how fast is the surface area increasing whenthe length of the edge in 30 cm ?

Answer 1

The rate at which the surface area of a cube is increasing when the length of the edge is 30 cm is 3600 cm²/min.

Step-by-step explanation:

The volume of a cube is given by V = s³, where s is the length of the side of the cube.

Since the volume is increasing at a rate of 10 cm³/min, we can express this as dV/dt = 10.

We want to find the rate at which the surface area (SA) is increasing when the length of the edge is 30 cm.

The surface area of a cube is given by SA = 6s².

To find the rate of change of SA, we differentiate both sides of the equation with respect to time:

d(SA)/dt = d(6s²)/dt

= 12s(ds/dt).

Substituting s = 30 and dV/dt = 10, we can solve for d(SA)/dt:

d(SA)/dt = 12s(ds/dt)

= 12(30)(10)

= 3600 cm²/min