Question

If the surface area of a cube is increasing at a rate of 3.6 cm²/sec, retaining its shape; then the rate of change of its volume (in cm³/sec), when the length of a side of the cube is 10 cm, is : 

(1) 9 

(2) 18 

(3) 10 

(4) 20

Answer 1

(a) 9

\(\frac{d}{dt}\)(6a²) = 3.6 ⇒ 12a \(\frac{da}{dt}\) = 3.6

a\(\frac{da}{dt}\) = 0.3

\(\frac{dv}{dt}\) = \(\frac{d}{dt}\)(a³) 

= 3a \((a\frac{da}{dt})\)

= 3 x 10 x 0.3 

= 9