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If the surface area of a cube increases at a rate of 24cm^2/s, then the rate at which its volume increases with respect to time if its side a=2cm, will be: |
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Answer» Here, side of the cube is `a = 2cm` . Then, Surface area of the cube `(S) = 6a^2` `:. (dS)/dt = 12a*(da)/dt = 24` `=>12**2((da)/dt) = 24 =>(da)/dt = 1` Now, volume of the cube `(V)= a^3` `:.` Rate of change of volume,`(dV)/dt = 3a^2(da)/dt = 3**(2)^2**1 = 12 (cm^3)/sec` |
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