MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 24

MEDIUM

12th CBSE

IMPORTANT

Earn 100

Sand is being poured onto a conical pile at the constant rate of $50 {cm}^{3} / minute$ 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?

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 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 = \frac{2}{3} x^{3} + 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

y^{2} = 8 x

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 {cm}^{3} / \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 {cm}^{3} / \sec

. Find the rate of change of its surface area at the instant when radius is

5 cm

?

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 30

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 rate of change of the perimeter ?

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 30

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 area of the rectangle.

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 13 - Derivative as a Rate Measurer>EXERCISE>Q 31

A circular disc of radius

3 cm

is being heated. Due to expansion, its radius increases at the rate of

0.05 cm / \sec

. Find the rate at which its area is increasing when radius is

3.2 cm

.