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
A point source of light is hung 30 feet directly above a straight horizontal path on which a man of 6 feet in height is walking. How fast will the man’s shadow lengthen and how fast will the tip of shadow move when he is walking away from the light at the rate of 100 ft/min.
A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.
The total revenue in rupees received from the sale of x units of a product is given by R(x) = 3x2 + 36x + 5. The marginal revenue, when x = 15 is ______.
The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.
The volume of a sphere is increasing at the rate of 3 cubic centimeter per second. Find the rate of increase of its surface area, when the radius is 2 cm
The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (Marginal revenue). If the total revenue (in rupees) recieved from the sale of x units of a product is given by R(x) = 3x2 + 36x + 5, find the marginal revenue, when x = 5, and write which value does the question indicate ?
A particle moves along the curve y = x2 + 2x. At what point(s) on the curve are the x and y coordinates of the particle changing at the same rate?
Find an angle θ which increases twice as fast as its cosine ?
The top of a ladder 6 metres long is resting against a vertical wall on a level pavement, when the ladder begins to slide outwards. At the moment when the foot of the ladder is 4 metres from the wall, it is sliding away from the wall at the rate of 0.5 m/sec. How fast is the top-sliding downwards at this instance?
How far is the foot from the wall when it and the top are moving at the same rate?
A balloon in the form of a right circular cone surmounted by a hemisphere, having a diameter equal to the height of the cone, is being inflated. How fast is its volume changing with respect to its total height h, when h = 9 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 52 m/sec, find the rate at which the string is being paid out.
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 radius of a circle is increasing at the rate of 0.5 cm/sec. Find the rate of increase of its circumference ?
The side of an equilateral triangle is increasing at the rate of \[\frac{1}{3}\] cm/sec. Find the rate of increase of its perimeter ?
The amount of pollution content added in air in a city due to x diesel vehicles is given by P(x) = 0.005x3 + 0.02x2 + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above questions ?
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
If the rate of change of area of a circle is equal to the rate of change of its diameter, then its radius is equal to
If s = t3 − 4t2 + 5 describes the motion of a particle, then its velocity when the acceleration vanishes, is
The diameter of a circle is increasing at the rate of 1 cm/sec. When its radius is π, the rate of increase of its area is
Evaluate: `int (x(1+x^2))/(1+x^4)dx`
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?
If the area of a circle increases at a uniform rate, then prove that perimeter varies inversely as the radius
A ladder, 5 meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is ______.
The instantaneous rate of change at t = 1 for the function f (t) = te-t + 9 is ____________.
The radius of a cylinder is increasing at the rate of 3 m/s and its height is decreasing at the rate of 4 m/s. The rate of change of volume when the radius is 4 m and height is 6 m, is ____________.
A particle is moving along the curve x = at2 + bt + c. If ac = b2, then particle would be moving with uniform ____________.
A particle moves along the curve 3y = ax3 + 1 such that at a point with x-coordinate 1, y-coordinate is changing twice as fast at x-coordinate. Find the value of a.
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?
