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:
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:
Option 1 -
9
Option 2 -
18
Option 3 -
10
Option 4 -
20
Asked by Shiksha User
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1 Answer
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Correct Option - 1
Detailed Solution:S = 6a² => dS/dt = 12a * da/dt = 3.6
=> 12 (10) da/dt = 3.6
=> da/dt = 0.03
V = a³ => dV/dt = 3a² * da/dt
= 3 (10)² * (3/100) = 9
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