The edge of a cube is increasing at the rate | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the edge of the cube be $a$ and its volume be $V$.Given that the rate of change of the edge is $\frac{da}{dt} = 5 \, cm/\sec$.The volume of a

Vedclass · Accepted Answer

$2160$

Vedclass · Answer

(B) Let the edge of the cube be $a$ and its volume be $V$.Given that the rate of change of the edge is $\frac{da}{dt} = 5 \, cm/\sec$.The volume of a cube is given by $V = a^3$.Differentiating both sides with respect to time $t$,we get:$\frac{dV}{dt} = 3a^2 \frac{da}{dt}$.Substitute the given values $a = 12 \, cm$ and $\frac{da}{dt} = 5 \, cm/\sec$ into the equation:$\frac{dV}{dt} = 3 	imes (12)^2 	imes 5$$\frac{dV}{dt} = 3 	imes 144 	imes 5$$\frac{dV}{dt} = 432 	imes 5 = 2160 \, cm^3/\sec$.Thus,the volume of the cube is increasing at the rate of $2160 \, cm^3/\sec$.

The edge of a cube is increasing at the rate of $5 \, cm/\sec$. How fast is the volume of the cube increasing when the edge is $12 \, cm$ long? (in $cm^3/\sec$)

Similar Questions

The vertical angle of a right circular cone is $60^{\circ}$. If water is being poured into the cone at the rate of $\frac{1}{\sqrt{3}} \text{ m}^3/\text{min}$, then the rate $(\text{m/min})$ at which the radius of the water level is increasing when the height of the water level is $3 \text{ m}$ is

$A$ ball thrown vertically upwards falls back on the ground after $6 \, s$. Assuming that the equation of motion is of the form $s = ut - 4.9t^2$,where $s$ is in metres and $t$ is in seconds,find the initial velocity $u$ at $t = 0$ in $m/s$.

If $f(x) = 2x^{2}$,find $\frac{f(3.8) - f(4)}{3.8 - 4}$.

The side of a square sheet of metal is increasing at the rate of $3 \text{ cm/min}$. At what rate is the area increasing when the length of the side is $6 \text{ cm}$?

Find the rate of change of the area of a circle with respect to its radius $r$ when $r = 3 \text{ cm}$. (in $\pi \text{ cm}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module