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 rate of change of the area of a circle with respect to its radius $r$ at $r = 2 \text{ cm}$ is:

$A$ particle is in motion along a curve $12 y = x^{3}$. The rate of change of its ordinate exceeds that of its abscissa when:

The radius of a cylinder is increasing at the rate of $2 \text{ cm/sec}$ and its height is decreasing at the rate of $3 \text{ cm/sec}$. Find the rate of change of volume when the radius is $3 \text{ cm}$ and the height is $5 \text{ cm}$.

$A$ kite is $120 \ m$ high and $130 \ m$ of string is out. If the kite is moving away horizontally at the rate of $39 \ m/sec$,then the rate at which the string is being paid out is:

Water is running into a hemispherical bowl of radius $180 \text{ cm}$ at the rate of $108 \text{ dm}^3/\text{min}$. How fast is the water level rising when the depth of the water in the bowl is $120 \text{ cm}$? $(1 \text{ dm} = 10 \text{ cm})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module