MEDIUM
12th CBSE
IMPORTANT
Earn 100

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?

Important Questions on Derivative as a Rate Measurer

MEDIUM
12th CBSE
IMPORTANT
MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 22
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.
MEDIUM
12th CBSE
IMPORTANT
MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 23
The volume of metal in a hollow sphere is constant. If the inner radius is increasing at the rate of 1 cm/sec, find the rate of increase of the outer radius when the radii are 4 cm and 8 cm respectively.
MEDIUM
12th CBSE
IMPORTANT
MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 24
Sand is being poured onto a conical pile at the constant rate of 50 cm3/minute such that the height of the cone is always one half of the radius of its base. How fast is the height of the pile increasing when the sand is 5 cm deep?
MEDIUM
12th CBSE
IMPORTANT
MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 25
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.
MEDIUM
12th CBSE
IMPORTANT
MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 26
A particle moves along the curve y=23x3+1. Find the points on the curve at which the y-coordinate is changing twice as fast as the x-coordinate.
EASY
12th CBSE
IMPORTANT
MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 27
Find the point on the curve y2=8x for which the abscissa and ordinate change at the same rate.
MEDIUM
12th CBSE
IMPORTANT
MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 28
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?
MEDIUM
12th CBSE
IMPORTANT
MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 29
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?