Rate of Change of Quantities MCQs

If y = x², then the rate of change of y with respect to x is:

• 2x

• x

• x²

• 1

If the radius of a circle is increasing at the rate of 3 cm/s, then the rate of change of area when radius is 5 cm is:

• 30π cm²/s

• 15π cm²/s

• 5π cm²/s

• 45π cm²/s

If the side of a square is increasing at the rate of 4 cm/s, then the rate of change of area is:

• 4x

• 8x

• 16

• 8

The volume V of a cube of side x is changing with respect to time. What is dV/dt?

• 3x²·dx/dt

• x³·dx/dt

• 2x·dx/dt

• 6x·dx/dt

The rate of change of volume of a sphere with respect to its radius is:

• 4πr²

• (4/3)πr³

• 2πr

• 6πr

If the length of a rectangle is increasing and breadth is constant, then the area increases at the rate:

• b·(dl/dt)

• l·(db/dt)

• (dl/dt)·(db/dt)

• l + b

The surface area S of a sphere is 4πr². Then dS/dt is:

• 8πr·(dr/dt)

• 2πr·(dr/dt)

• 4π·(dr/dt)

• πr²·(dr/dt)

If the distance s travelled in time t is s = 5t², then the velocity is:

• 10t

• 5t

• 2t

• 25t

A balloon is rising vertically at 4 m/s, and a boy is standing 30 m away from the point of lift-off. How fast is the distance between the boy and balloon increasing when the balloon is 40 m high?

• 5 m/s

• 3 m/s

• 4 m/s

• 6 m/s