Calculus

Application of Derivatives

Medium

common

The volume of a cube is increasing at the rate of 27 cm $^3$ /s. How fast is the surface area increasing when the length of the cube is 12 cm.

9 cm $^2$ /s

$\frac{9}{4}$ cm $^2$ /s

$\frac{4}{9}$ cm $^2$ /s

$\frac{9}{2}$ cm $^2$ /s

✅ Correct Option: 1

Volume $V = a^3$ , so $dV/dt = 3a^2(da/dt)$ . With $dV/dt = 27$ and $a = 12$ : $27 = 3(144)(da/dt)$ , giving $da/dt = 1/16$ . Surface area $S = 6a^2$ , so $dS/dt = 12a(da/dt) = 12(12)(1/16) = 9$ cm $^2$ /s.

2026: 21 May Shift 2

Which of the following functions are strictly decreasing on $\left(0, \dfrac{\pi}{2}\right)$ ?

A. $\cos x$

B. $-\cot x$

C. $\cos 2x$

D. $\sin x$

Choose the correct answer from the options given below:

2022: 4 Aug Shift 1

The slope of normal to the curve $y = kx^2 - 3x + 2$ at $x = \frac{1}{2}$ is 5. The value of 'k' is

2022: 7 Aug Shift 2

The slope of the tangent drawn at the point whose x coordinates is 2 on the curve $y = x|x|$ .

2025: 15 May Shift 1

Which of the following functions are increasing on $x \in \left(0, \frac{\pi}{2}\right)$ ?

(A) $f(x) = \sin x$

(B) $f(x) = \cos x$

(D) $f(x) = \cos 3x$

Choose the correct answer from the options given below:

2025: 2 June Shift 1

The function $f(x) = 2\log_e(x-2) - x^2 + 4x + 1, (x > 2)$ is increasing on the interval:

2025: 29 May Shift 2

The rate of change of volume of a sphere with respect to its surface area, when the radius is 6cm is:

The volume of a cube is increasing at the rate of 27 cm3^33/s. How fast is the surface area increasing when the length of the cube is 12 cm.

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The volume of a cube is increasing at the rate of 27 cm $^3$ /s. How fast is the surface area increasing when the length of the cube is 12 cm.