Advertisements
Advertisements
प्रश्न
Side of an equilateral triangle expands at the rate of 2 cm/sec. The rate of increase of its area when each side is 10 cm is
पर्याय
\[10\sqrt{2} \ {cm}^2 /\sec\]
\[10\sqrt{3} {cm}^2 /\sec\]
10 cm2/sec
5 cm2/sec
Advertisements
उत्तर
\[10\sqrt{3} \ {cm}^2 /\sec\]
\[\text { Letxbe the side andAbe the area of the equilateral triangle at any timet.Then },\]
\[A = \frac{\sqrt{3}}{4} x^2 \]
\[ \Rightarrow \frac{dA}{dt} = 2 \times \frac{\sqrt{3}}{4} x^{} \frac{dx}{dt}\]
\[\Rightarrow\frac{dA}{dt}=\frac{\sqrt{3}}{2}\times2\times10\]
\[\Rightarrow\frac{dA}{dt}=10\sqrt{3} \ {cm}^2 /sec\]
APPEARS IN
संबंधित प्रश्न
The volume of a cube is increasing at the rate of 8 cm3/s. How fast is the surface area increasing when the length of an edge is 12 cm?
A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.
Find the rate of change of the total surface area of a cylinder of radius r and height h, when the radius varies?
Find the rate of change of the area of a circular disc with respect to its circumference when the radius is 3 cm ?
Find the rate of change of the volume of a cone with respect to the radius of its base ?
The total cost C (x) associated with the production of x units of an item is given by C (x) = 0.007x3 − 0.003x2 + 15x + 4000. Find the marginal cost when 17 units are produced ?
The side of a square is increasing at the rate of 0.2 cm/sec. Find the rate of increase of the perimeter of the square.
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?
A man 160 cm tall, walks away from a source of light situated at the top of a pole 6 m high, at the rate of 1.1 m/sec. How fast is the length of his shadow increasing when he is 1 m away from the pole?
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?
A man 2 metres high walks at a uniform speed of 6 km/h away from a lamp-post 6 metres high. Find the rate at which the length of his shadow increases ?
The radius of a cylinder is increasing at the rate 2 cm/sec. and its altitude is decreasing at the rate of 3 cm/sec. Find the rate of change of volume when radius is 3 cm and altitude 5 cm.
Find the point on the curve y2 = 8x for which the abscissa and ordinate change at the same rate ?
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 ?
The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. How far is the area increasing when the side is 10 cms?
If the rate of change of volume of a sphere is equal to the rate of change of its radius, find the radius of the sphere ?
A ladder, 5 metre long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides down wards at the rate of 10 cm/sec, then find the rate at which the angle between the floor and ladder is decreasing when lower end of ladder is 2 metres from the wall ?
A cone whose height is always equal to its diameter is increasing in volume at the rate of 40 cm3/sec. At what rate is the radius increasing when its circular base area is 1 m2?
The radius of a sphere is increasing at the rate of 0.2 cm/sec. The rate at which the volume of the sphere increase when radius is 15 cm, is
The volume of a sphere is increasing at the rate of 4π cm3/sec. The rate of increase of the radius when the volume is 288 π cm3, is
Each side of an equilateral triangle is increasing at the rate of 8 cm/hr. The rate of increase of its area when side is 2 cm, is
If s = t3 − 4t2 + 5 describes the motion of a particle, then its velocity when the acceleration vanishes, is
The equation of motion of a particle is s = 2t2 + sin 2t, where s is in metres and t is in seconds. The velocity of the particle when its acceleration is 2 m/sec2, 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
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
In a sphere the rate of change of surface area is
A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of
Evaluate: `int (x(1+x^2))/(1+x^4)dx`
For the curve y = 5x – 2x3, if x increases at the rate of 2 units/sec, then how fast is the slope of curve changing when x = 3?
The rate of change of volume of a sphere with respect to its surface area, when the radius is 2 cm, is ______.
A spherical ball of salt is dissolving in water in such a manner that the rate of decrease of the volume at any instant is proportional to the surface. Prove that the radius is decreasing at a constant rate
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 ______.
What is the rate of change of the area of a circle with respect to its radius when, r = 3 cm
The median of an equilateral triangle is increasing at the ratio of `2sqrt(3)` cm/s. Find the rate at which its side is increasing.
