Home
Class 12
MATHS
Water is dropped at the rate of 2 m^(3)/...

Water is dropped at the rate of 2 `m^(3)//s` into a cone of semi-vertical angle of `45^(@)`. The rate at which periphery of water surface changes when height of water in the cone is 2 m, is

A

0.5 m/s

B

2 m/s

C

3 m/s

D

1 m/s

Text Solution

Verified by Experts

The correct Answer is:
D
Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

A water tank is in the shape of a right circular cone with its axis vertical and vertex down. Its height and diameter are same. Water is powered into it at a constant rate of 2m^3//minute . Find the rate at which water level is increasing when depth of water in the tank is 6m.

If water is poured into an inverted hollow cone whose semi-vertical angle is 30^(@) , show that its depth (measured along the axis) increases at the rate of 1 cm/s. Find the rate at which the volume of water increases when the depth is 24 cm.

Knowledge Check

  • The radius of the base of a cone is increasing at the rate of 3 cm/min and the altitude is decreasing at the rate of 4 cm/min. The rate of change of lateral surface when the radius is 7 cm and altidue is 24 cm is

    A
    108 `pi cm^(2)//min`
    B
    `7 pi cm^(2)//min`
    C
    `27 pi cm^(2)//min`
    D
    none of these

  • The rate of change of the volume of a sphere w.r.t. its surface area, when the radius is 2 cm, is

    A
    1
    B
    2
    C
    3
    D
    4

  • The radius of the base of a cone is increasing at the rate of 3 cm/minute and the altitude is decreasing at the rate of 4 cm/minute. The rate f change of lateral surface when the radius = 7 cm and altitude = 24 cm, is

    A
    `54 pi cm^(2)//min`
    B
    `7 pi cm^(2)//min`
    C
    `27 pi cm^(2)//min`
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    Show that semi-vertical angle of right circular cone of given surface area and maximum volume is sin^-1(1/3) .

    Sand is pouring from a pipe at the rate of 12 cm^3 / s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast if the height of the sand cone increasing when the height is 4 cm ?'

    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

    A man is moving away from a tower 41.6 m high at a rate of 2 m/s. If the eye level of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of 30 m from the foot of the tower, is

    The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder, in cm^(3)//min , when the radius is 2 cm and the height is 3 cm is

    Home
    Profile