Let A be the area of a circle with radius r. If dr = 3, find dA dt when r = 1. dtA spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.2 cm/min. At what rate is the volume of the snowball decreasing when the radius is 12 cm. (Note the answer is a positive number). cm min Hint: The volume of a sphere of radius r is V =The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the triangle is increasing at a rate of 4.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7 centimeters and the area is 99 square centimeters? cm/minGravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cc-ne whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by 1 _ V=m% |:l ft min A rotating light is located 20 feet from a wall. The light complete: one rotation every 1 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wall. wall light Answer is a positive value. At noon, ship A15 21'} nautical miles due west of ship 5. ShipAis sailing west at 16 knots and ship E. is sailing north at 15 knots. How fast [in knots] is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.) A street light is at the top of a 10 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 35 ft from the base of the pole? ft secAn inverted pyramid is being filled with water at a constant rate of ?5 cubic centimeters per second. The pyramid, at the top. has the shape of a square with sides of length 7 cm and the height is 14 cm. Find the rate at which the 1Miter Level is rising when the water level is 2 cm. A circle is inside a square. The radius of the circle is decreasing at a rate of 1 meter per hour and the sides of the square are decreasing at a rate of 4 meters per hour. When the radius is 2 meters, and the sides are 19 meters. then how fast is the AREA outside the circle but inside the square changing? The rate of change of the area enclosed between the circle and the square is :] square meters per hour