The Total solution for NCERT class 6-12
The volume of a cube is increasing at therate of 8 cm3/s. How fast is the surface area increasing when thelength of an edge is 12 cm?
Let x be the length of a side, V bethe volume, and s bethe surface area of the cube.
Then, V = x3 and S = 6x2 where x isa function of time t.
Then, by using the chain rule, we have:
∴
Thus, when x =12 cm,
Hence, if the length of theedge of the cube is 12 cm, then the surface area is increasing at the rateof cm2/s.