EASY
12th CBSE
IMPORTANT
Earn 100

The side of a square sheet of a metal is increasing at a rate of 3 centimetres per minute. At what rate is the area increasing in cm2/s when the side is 10 cm long?

50% studentsanswered this correctly

Important Questions on Applications of Derivatives

EASY
12th CBSE
IMPORTANT

The radius of a spherical soap bubble is increasing at the rate of 0.2 cm/s. If the rate of increase of its surface area when the radius is 7 cm is k cm2/s, then find the value of k. (Take π=227)

{Write the answer in decimal form}

EASY
12th CBSE
IMPORTANT

The radius of an air bubble is increasing at the rate of 0.5 centimetre per second. At what rate is the volume of the bubble increasing in cm3/s when the radius is 1 centimetre? (Take π=3.14)

EASY
12th CBSE
IMPORTANT

The volume of a spherical balloon is increasing at the rate of 25 cubic centimetres per second. Find the rate of change of its surface in cm2/s at the instant when its radius is 5 cm.

EASY
12th CBSE
IMPORTANT
A balloon which always remains spherical is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate (in cm/s) at which the radius of the balloon is increasing when the radius is 15 cm. Use π=3.14        (Round off final answer to two decimal places and enter the value excluding units)
EASY
12th CBSE
IMPORTANT

The bottom of a rectangular swimming tank is 25 m by 40 m. Water is pumped into the tank at the rate of 500 cubic metres per minute. Find the rate at which the level of water in the tank is rising in m/min.

EASY
12th CBSE
IMPORTANT
A stone is dropped into a quiet lake and waves move in circles at a speed of 3.5 cm/s. At the instant when the radius of the circular wave is 7.5 cm, if the enclosed area is increasing at the rate of k cm2/s, then what is the value of k? (Take π = 227)
MEDIUM
12th CBSE
IMPORTANT

A 2 m tall man walks at a uniform speed of 5 km/h away from a 6 m high lamp post. Find the rate at which the length of his shadow increases in km/h.

MEDIUM
12th CBSE
IMPORTANT

An inverted cone has a depth of 40 cm and a base of radius 5 cm. Water is poured into it at a rate of 1.5 cubic centimetres per minute. The rate at which the level of water in the cone is rising when the depth is 4 cm in cm/sec is ab cm/sec, where a andb are smallest positive integers . Finda+b.  (Take π=227)