1. A spherical snowball is melting. Its radius is decreasing at 0.2 cm per hour when the radius is 15 cm. How fast is its volume decreasing at that time?
2. A potter forms a piece of clay into a cylinder. As he rolls it, the length, , of the cylinder increases and the radius, , decreases. If the length of the cylinder is increasing at 0.1 cm per second, find the rate at which the radius is changing when the radius is 1 cm and the length is 5 cm.
3. A certain quantity of gas occupies a volume of 20cc at a pressure of 1 atmosphere. The gas expands without the addition of heat, so, for some constant , its pressure, , and volume, , satisfy the equation . (a) Find the rate of change of pressure with respect to volume. (b) The volume is increasing at 2cc/min when the volume is 30cc. At that moment, is the pressure increasing or decreasing? How fast?
4. (a) A hemispherical bowl of radius 10cm contains water to a depth of cm. Find the radius of the surface of the water as a function of . (b) The water level drops at a rate of 0.1 cm per hour. At the what rate is the radius of the water decreasing when the depth is 5 cm?
- Two planes leave an airport at the same time, one flying at 300 km/h and the other at 420 km/h. The angle between their flight paths is 75 degrees. After three hours, how far apart are they?
- From the top of a building 10 m tall, the angle of elevation to the top of a flagpole is 11 degrees. At the base of the building, the angle of elevation to the top of the flagpole is 39 degrees. Find the height of the flagpole.
- In quadrilateral ABCD, AB=3, BC=4, CD=5, and DA=6. The length of diagonal BD is 7. Find the length of the other diagonal.