Volume V=a3, so dV/dt=3a2(da/dt). With dV/dt=27 and a=12: 27=3(144)(da/dt), giving da/dt=1/16. Surface area S=6a2, so dS/dt=12a(da/dt)=12(12)(1/16)=9 cm2/s.
The volume of a cube is increasing at the rate of 27 cm3/s. How fast is the surface area increasing when the length of the cube is 12 cm.
Held on 23 May 2023 · Verified 13 Jul 2026.
9 cm2/s
49 cm2/s
94 cm2/s
29 cm2/s
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