Related Rates

A ladder is 10 meters long and is leaning against a wall. If the bottom of the ladder is sliding away from the wall at a rate of 2 m/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 meters from the wall?

A spherical ballon is being inflated at a rate of $$100\ \frac{cm^3}{\sec}.$$ How fast is the radius of the ballon increasing when the diameter is $$50\ cm?$$

A $$13-foot$$ ladder is leaning against a wall when its base starts to slide away from the wall. By the time its base is $$12\ ft$$ from the wall, the base is moving at the rate of $$5\ \frac{ft}{\sec}.$$ How fast is the top of the ladder sliding down the wall then?

All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing each edge is 1 centimeter.

A balloon is being inflated and its volume is increasing at a rate of 100 cubic centimeters per second. How fast is the radius of the balloon increasing when the radius is 5 centimeters? (Use the formula for the volume of a sphere: $$V = \frac{4}{3}\pi r^3$$ )

Given: Water slowly evaporates from a circular shaped puddle. The area of the puddle decreases at a rate of  $$36\pi\ \frac{in^2}{hr}$$  . Assuming the puddle retains its circular shape, at what rate is the radius of the puddle changing when the radius is 5 in?

Spherical snowball is rolled in fresh snow, causing it to grow so that its radius increases at a rate of 2 in/sec. How fast is the volume of the snowball increasing when the radius is 2 in?

Volume of a sphere = $$\frac{4}{3}\pi r^3$$

A pebble is thrown into a pond forming a ripple whose radius increases at a rate of 4 in/sec. How fast is the area of the ripple changing when the radius is 1 foot?

 A piece of ice cut into the shape of a cube melts uniformly so that its volume decreases $$3\ \frac{cm^3}{\sec}$$ . How fast its surface area decreasing when the edge of the cube is 5cm?