Verified Solution • 2025–26 Session moderate

QJEEM20Mac2b2: JEE Main 2020 Mathematics - Class 12 JEEM20Mac2b2 Solution: If the surface area of a cube is increasing at a rate of 3.6 cm …

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 :

Multiple Choice Options

  • A 9
  • B 10
  • C 18
  • D 20

Step-by-Step Verified Solution

For cube of side 'a'

A = 6a2 and V = a3

Given dAdt=3.6{{dA} \over {dt}} = 3.6

⇒\Rightarrow 12adadt12a{{da} \over {dt}} = 3.6

dVdt=3a2.dadt=3a2(3.612a){{dV} \over {dt}} = 3{a^2}.{{da} \over {dt}} = 3{a^2}\left( {{{3.6} \over {12a}}} \right)

at a = 10

dVdt=9{{dV} \over {dt}} = 9

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