Quiz (Related Rates)

Show all work and justify each step. In particular, label each variable, sketch a diagram, and write a sentence which describes your answer to each question.

(1) All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each side is (a) 1 centimeter and (b) 10 centimeters?

(2) A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep?

(3) A balloon rises at a rate of 3 meters per second from a point on the ground 30 meters from an observer. What is the rate of change of the angle of elevation of the balloon from the observer when the balloon is 30 meters above the ground?

(4) A trough is 10 feet long and its ends have the shape of an isosceles triangles that are 3 feet across at the top and have a height of 1 foot. If the trough is filled with water at a rate of how fast does the water level rise when the water is 6 inches deep?

(5) A water trough is 10 m long and a cross section has the shape of an isosceles trapezoid that is 30 centimeters wide at the bottom, 80 centimeters wide at the top, and has height 50 centimeters. If it is being filled with water at the rate of how fast is the water level rising when the water is 30 centimeters deep?

Cite this as:
Related Rates Quiz
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/related-rates-quiz.html