Calculus

Application of Derivatives

Medium

core

The volume of a cube is increasing at the rate 9 $cm^3/s$ . How fast is the surface area increasing when the length of an edge is 10 cm ?

3.6 $cm^2/s$

36 $cm^2/s$

120 $cm^2/s$

2.4 $cm^2/s$

✅ Correct Option: 1

With $V = a^3$ , $\dfrac{dV}{dt} = 3a^2\dfrac{da}{dt} = 9$ , so at $a=10$ , $\dfrac{da}{dt} = \dfrac{9}{300} = 0.03$ cm/s.

With $S = 6a^2$ , $\dfrac{dS}{dt} = 12a\dfrac{da}{dt} = 12(10)(0.03) = 3.6$ $cm^2/s$ .

2025: 16 May Shift 1

For x ∈ ℝ - {0}, the function f(x) = $\frac{3}{x}$ + 7 is decreasing when

2022: 23 Aug Shift 1

Minimum value of D is :

2023: 22 May Shift 3

The appropriate change in the volume V of a cube of side $x$ metres caused by increasing the side by 2% is :

2022: 10 Aug Shift 1

The absolute maximum value of $y = x^3 - 3x + 2$ , $0 \leq x \leq 2$ , is

2023: 15 June Shift 2

The value of C which satisfies Rolle's Theorem for $f(x) = \sin^4 x + \cos^4 x$ in $\left[0, \frac{\pi}{2}\right]$ . Then C is :

2025: 29 May Shift 2

The total cost function is given by $c(x) = \frac{1}{3}x^3 - 5x^2 + 30x - 15$ and selling price per unit is Rs.6. The profit is maximum if the value of x is:

The volume of a cube is increasing at the rate 9 cm3/scm^3/scm3/s. How fast is the surface area increasing when the length of an edge is 10 cm ?

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The volume of a cube is increasing at the rate 9 $cm^3/s$ . How fast is the surface area increasing when the length of an edge is 10 cm ?