Advertisements
Advertisements
प्रश्न
The Volume of cube is increasing at the rate of 9 cm 3/s. How fast is its surfacee area increasing when the length of an edge is 10 cm?
Advertisements
उत्तर
`(dV)/dt = 9 "cm"^"3//sec x = 10 cm` (given)
`V = x^3`
`(dV)/dt = 3x^2 dx/dt`
`9/(3x^2) = dx/dt`
Now, `s = 6x^2`
`(ds)/dt = 12x xx dx/dt`
`(ds)/dt = 12 xx 10 xx 9/(3xx10xx10)`
`= (12 xx 9)/(3xx 10) = 36/10`
`= 3.6 cm^2//sec`
APPEARS IN
संबंधित प्रश्न
If y = f (u) is a differential function of u and u = g(x) is a differential function of x, then prove that y = f [g(x)] is a differential function of x and `dy/dx=dy/(du) xx (du)/dx`
Find the rate of change of the area of a circular disc with respect to its circumference when the radius is 3 cm ?
The radius of an air bubble is increasing at the rate of 0.5 cm/sec. At what rate is the volume of the bubble increasing when the radius is 1 cm?
A stone is dropped into a quiet lake and waves move in circles at a speed of 4 cm/sec. At the instant when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?
The surface area of a spherical bubble is increasing at the rate of 2 cm2/s. When the radius of the bubble is 6 cm, at what rate is the volume of the bubble increasing?
A particle moves along the curve y = (2/3)x3 + 1. Find the points on the curve at which the y-coordinate is changing twice as fast as the x-coordinate ?
The volume of a cube is increasing at the rate of 9 cm3/sec. How fast is the surface area increasing when the length of an edge is 10 cm?
The volume of a spherical balloon is increasing at the rate of 25 cm3/sec. Find the rate of change of its surface area at the instant when radius is 5 cm ?
The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rates of change of the perimeter.
If a particle moves in a straight line such that the distance travelled in time t is given by s = t3 − 6t2+ 9t + 8. Find the initial velocity of the particle ?
A cylindrical vessel of radius 0.5 m is filled with oil at the rate of 0.25 π m3/minute. The rate at which the surface of the oil is rising, is
The distance moved by the particle in time t is given by x = t3 − 12t2 + 6t + 8. At the instant when its acceleration is zero, the velocity is
The altitude of a cone is 20 cm and its semi-vertical angle is 30°. If the semi-vertical angle is increasing at the rate of 2° per second, then the radius of the base is increasing at the rate of
The volume of a sphere is increasing at 3 cm3/sec. The rate at which the radius increases when radius is 2 cm, is
A man of height 6 ft walks at a uniform speed of 9 ft/sec from a lamp fixed at 15 ft height. The length of his shadow is increasing at the rate of
A ladder 13 m long is leaning against a vertical wall. The bottom of the ladder is dragged away from the wall along the ground at the rate of 2 cm/sec. How fast is the height on the wall decreasing when the foot of the ladder is 5 m away from the wall?
A kite is moving horizontally at a height of 151.5 meters. If the speed of kite is 10 m/s, how fast is the string being let out; when the kite is 250 m away from the boy who is flying the kite? The height of boy is 1.5 m.
Two men A and B start with velocities v at the same time from the junction of two roads inclined at 45° to each other. If they travel by different roads, find the rate at which they are being seperated.
The radius of a circle is increasing uniformly at the rate of 3 cm per second. Find the rate at which the area of the circle is increasing when the radius is 10 cm.
A man 1.6 m tall walks at the rate of 0.3 m/sec away from a street light that is 4 m above the ground. At what rate is the tip of his shadow moving? At what rate is his shadow lengthening?
A spherical balloon is filled with 4500π cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is ______.
An edge of a variable cube is increasing at the rate of 10 cm/sec. How fast will the volume of the cube increase if the edge is 5 cm long?
Given that `1/y + 1/x = 1/12` and y decreases at a rate of 1 cms–1, find the rate of change of x when x = 5 cm and y = 1 cm.
A kite is being pulled down by a string that goes through a ring on the ground 8 meters away from the person pulling it. If the string is pulled in at 1 meter per second, how fast is the kite coming down when it is 15 meters high?
If a quantity \(y\) varies with another quantity \(x\) based on the rule \(y=f(x)\), which expression represents the rate of change of \(y\) with respect to \(x\)?
What does evaluating \[\left.\frac{dy}{dx}\right|_{x=x_0}\] give?
For the Chain Rule for Rates \[\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}\], which condition is required?
What does a positive derivative mean for a quantity?
What does a negative derivative mean for a quantity?
