The edge of a cube is increasing at a rate of 7 cm/s. The rate of change of area of the cube when its side is 3 cm is: Option 1: 525 cm²/s Option 2: 225 cm²/s Option 3: 255 cm²/s Option 4: 252 cm²/s

Answer: 252 cm²/s. Solution: The edge of a cube is increasing at a rate of 7 cm/s. The current side length is 3 cm. Surface Area of a cube is given by: A = 6a^2 where a is the side of the cube. Differentiating both sides with respect to time: dA/dt = 6 x 2a x da/dt dA/dt = 12a x da/dt Given: a = 3 cm da/dt = 7 cm/s Substituting these values: dA/dt = 12 x 3 x 7 dA/dt = 36 x 7 dA/dt = 252 cm²/s Therefore, the rate of change of surface area of the cube is 252 cm²/s.

Calculus

Application of Derivatives

Medium

core

The edge of a cube is increasing at a rate of 7 cm/s. The rate of change of area of the cube when its side is 3 cm is:

525 cm²/s

225 cm²/s

255 cm²/s

252 cm²/s

✅ Correct Option: 4

The edge of a cube is increasing at a rate of 7 cm/s. The current side length is 3 cm.

Surface Area of a cube is given by:

$A = 6a^2$

where $a$ is the side of the cube.

Differentiating both sides with respect to time:

$\dfrac{dA}{dt} = 6 \times 2a \times \dfrac{da}{dt}$

$\dfrac{dA}{dt} = 12a \times \dfrac{da}{dt}$

Given:

$a = 3$ cm

$\dfrac{da}{dt} = 7$ cm/s

Substituting these values:

$\dfrac{dA}{dt} = 12 \times 3 \times 7$

$\dfrac{dA}{dt} = 36 \times 7$

$\dfrac{dA}{dt} = 252$ cm²/s

Therefore, the rate of change of surface area of the cube is 252 cm²/s.

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The function $f(x) = (x - 1)(x + 1)^2$ has

List-I	List-II
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(B) A local minima at $x =$ ____	(II) 0
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The edge of a cube is increasing at a rate of 7 cm/s. The rate of change of area of the cube when its side is 3 cm is:

Solution

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