If the edge of a cube increases at the rate o | vedclass

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

Question

(B) Let $a$ be the edge of the cube and $V$ be its volume.Given that the rate of change of the edge is $\frac{da}{dt} = 60 \, cm/s$.The volume of a cu

Vedclass · Accepted Answer

$1458000$

Vedclass · Answer

(B) Let $a$ be the edge of the cube and $V$ be its volume.Given that the rate of change of the edge is $\frac{da}{dt} = 60 \, cm/s$.The volume of a cube is given by $V = a^3$.Differentiating both sides with respect to time $t$,we get $\frac{dV}{dt} = 3a^2 \frac{da}{dt}$.Substituting the given values $a = 90 \, cm$ and $\frac{da}{dt} = 60 \, cm/s$:$\frac{dV}{dt} = 3 	imes (90)^2 	imes 60$$\frac{dV}{dt} = 3 	imes 8100 	imes 60$$\frac{dV}{dt} = 180 	imes 8100 = 1458000 \, cm^3/s$.Thus,the volume is increasing at the rate of $1458000 \, cm^3/s$.

If the edge of a cube increases at the rate of $60 \, cm/s$,at what rate is the volume increasing when the edge is $90 \, cm$ (in $cm^3/s$)?

Similar Questions

The side of a square piece is increasing at a rate of $4 \text{ cm/min}$. Find the rate at which the area is increasing when the side is $8 \text{ cm}$ long.

If the rate of change of $x$ is more than the rate of change of $y$ on the curve $x^3 = 12y$ for $x > 0$,then $x$ lies in the interval:

$A$ stone thrown vertically upwards has its motion described by the equation $s = 13.8t - 4.9t^2$,where $s$ is in meters and $t$ is in seconds. The velocity at $t = 1$ second will be ...... $m/s$.

Water is being poured into a cylindrical vessel with a radius of $2 \text{ cm}$ at a rate of $8 \text{ cm}^3/\text{s}$. The rate at which the height of the water is increasing is:

$A$ firm is manufacturing $2000$ items. It is estimated that the rate of change of production $P$ with respect to the additional number of workers $x$ is given by $\frac{dP}{dx} = 100 - 12\sqrt{x}$. If the firm employs $25$ more workers,then the new level of production of items is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module