4.4-4.5FormativeAssignment
.pdf
School
Blue Valley West High**We aren't endorsed by this school
Course
CALC 123
Subject
Mathematics
Date
Dec 19, 2024
Pages
2
Uploaded by UltraHornetPerson1239
AP Calculus BC 4.4 – 4.5 Formative Assignment Show all your work and provide reasonable justification for your solution. Be sure to completely simplify. Return on one pdf. Do not use a calculator on these problems. 1. A container has the shape of an open right circular cone, as shown below. The height of the container is 10 cmand the diameter of the opening is 10 cm. Water in the container is evaporating so that its depth his changing at the constant rate of െଷଵܿ݉/݄ݎ. (Note: The volume of a cone of height h and radius r is given by ܸ=ଵଷߨݎଶ݄.) a) Find the volume Vof water in the container when h= 5 cm. Indicate units of measure. b) Find the rate of change of the volume of water in the container, with respect to time, when h= 5 cm. Indicate units of measure. 2. An isosceles right triangle with legs of length shas area ܣ=ଵଶݏଶ. At the instant when ݏ=ξ32cm, the area of the triangle is increasing at a rate of 12 ܿ݉ଶݏ݁ܿΤ. At what rate is the length of the hypotenuse of the triangle increasing, in centimeters per second, at that instant? 3. The radius of a circle is increasing at a constant rate of 0.5 meter per second. What is the rate of increase in the circumference of the circle at the instant when the radius of the circle is 3 meters?
4. The radius r of a sphere is increasing at a constant rate of 0.04 cm per second. a. At the time when the radius of the sphere is 10 centimeters, what is the rate of increase of its volume? b. At the time when the volume of the sphere is 36ʌcubic centimeters, what is the rate of increase of the area of a cross section through the center of the sphere? c. At the time when the volume and the radius of the sphere are increasing at the same numerical rate, what is the radius? ܸ=ସଷߨݎଷܵ= 4ߨݎଶ5. The length of a solid cylindrical cord of elastic material is 32 inches. A circular cross section of the chord has a radius ½ inch. a. What is the volume, in cubic inches, of the chord? b. The chord is stretched lengthwise at a constant rate of 18 inches per minute. Assuming that the cord maintains a cylindrical shape and a constant volume, at what rate is the radius of the chord changing one minute after the stretching begins? Indicate units of measure.