Green Area The four circles in the figure above each have a radius of 3 units.  The centers of each circle form a square.  Find the area of the green shaded region to the nearest tenth of a unit.
October 17, 2005
Past Problems
	E-mail Solutions to: pow@umassd.edu
	Correct Solutions
	Bob Mitchell. Normal, IL Hamilton Hardison.  University of Georgia.  Athens, GA Radu  Ionescu. Montreal, Quebec, Canada. Roland Vyncke. Brugge, Belgium Tim Poe. Austin, TX Virginia Cornelius. Lafayette High School, Oxford, MS Brian Hetrick. UNH, Manchester, NH Marius Damian. Braila, Romania Michael Fang. Osceola Middle, Ocala, FL Omid Kohannim. UCLA, Los Angeles, CA Aristides Kyriakakis. Thessaloniki, Greece Timothy Yales. Westland, MI Francois Bonjean. Liege, Belgium Jerome Cherry. Mundare, Alberta, Canada Jerrold Greenberg. New York, NY Alan Leung. Mississippi School for Mathematics, Columbus, MS Lisa Schechner. Schreiber HS, Port Washington, NY Devan Lai. Saratoga High School, Saratoga, CA Can Oztoprak. Istanbul, Turkey Rohit Bollineni. Power Middle School, Farmington Hills, MI Sahit Bollineni. High Meadow Common Campus, Farmington Hills, MI Emil Lalov. Mathematical High School, Pleven, Bulgaria Frank McGartland.  Saskatoon, SK., Canada Abhijeet Singh. Rai Foundation Colleges, Mumbai, India Kavika Daga. JFK High School, Iselin, NJ Anna Li. Sandburg Middle School, Anoka, MN Chauhan Rakesh. New Delhi India Christian Romero. Carwise Middle School, Palm Harbor, FL Chris Money. Carwise Middle, Palm Harbor, FL Thomas Medal. Our Lady of Sorrows Catholic School, Toronto, Ontario, Canada Wu Ken. Salvador, Bahia, Brazil Gustavo Amorim. Pan American School of Bahia, Salvador, Bahia, Brazil Raphael Chalhub. Pan American School of Bahia, Salvador, Bahia, Brazil Raphael Leitz. Pan American School of Bahia, Salvador, Bahia, Brazil Katherine Baur. Pan American School of Bahia, Salvador, Bahia, Brazil Steigen Johnson. Pan American School of Bahia, Salvador, Bahia, Brazil Eugene Roytman. New York, NY Tauseef Anam. Lakeview Academy, Gainesville, GA Christopher Thomas. New York, NY Roger Steffens. Atlanta, GA Ashvin Swaminathan. Harker Elementary School, San Jose, CA Maggie Schoening. Dartmouth High, Dartmouth, MA Peter  Moynahan. Rye Junior High, Rye, NH Asher Tuggle. Homes schooled, Colorado Springs, CO Sau Wai. Pan American School of Bahia, Salvador, Bahia, Brazil Jeff Stobbe. Muskego, WI Jon Eisenberg. Dartmouth High School, MA Seana McKee. Dartmouth High School, Dartmouth, MA Spencer Lindsay. Governor John Carver School, Carver, MA Jon Lewis. UNB, Fredericton, New Brunswick, Canada Viktor Elbert. Franklin High School, Reisterstown, MD Graham Anderson, Faith Lutheran College, Plainland, Qld Australia BCLUW High School Mathletes.  BCLUW High School, Conrad, IA David Lu. NYC Aaron Rose. Hastings Middle School, Fairhaven, MA Thomas Medal. Our Lady of Sorrows Catholic School, Toronto, Ontario, Canada Sarah Chen. Marie Curie Middle School, New York, NY Tanvi Rastogi. Bridgewater-Raritan High School, Bridgewater, NJ. Charles Keebaugh. Colorado Springs, CO Praveen Nandamuru. Brookstone School, Columbus, GA Ed Wern. Raj Patel. Palm Harbor, FL Nathan Caldwell. DeLaura Middle School, Satellite Beach, FL Abigail Finger. Dartmouth High School, Dartmouth, MA Minray Yang. Carwise Middle School Aashrita Mangu. South Pasadena Middle School, South Pasadena, CA Gavin Tse. South Pasadena Middle School, South Pasadena, CA Brianna Loo. South Pasadena Middle School. South Pasadena, CA Michelle Lam. South Pasadena Middle School, South Pasadena, CA katie meade. Rye Junior High, Rye, NH Mateo Kestenbaum. Dartmouth High School, Dartmouth, MA Minray Yang. Carwise Middle School David Shi. JLS Middle School, Palo Alto, CA Sagar Patel. Broookstone Schoool, Columbus, GA Alstyne Gravlee. St. Luke Middle School, Columbus, GA Ben Messier. Dartmouth, MA Vincent Dang. Stanton College Preparatory School, Jacksonville, FL Alyson Deleeuw. Rye Jr High, Rye, NH Alexis Cambra. Fairhaven Public Schools, Fairhaven, MA Paige Cambra. Fairhaven Public Schools, Fairhaven, MA Dave Barron.  Chelmsford High School, Chelmsford, MA Blakeley Coull. St. Luke School, Columbus, GA John Jones Jr. Belleville East High School, Belleville, IL Julie Strang. Valencia Community College, Kissimmee, FL Roger Ouyang. Bluffs Elementary School, San Diego, CA Sky Su. Brooklawn Middle School, Parsippany, NJ Rachel Bier. Dartmouth High, Dartmouth, MA Maura MacKenzie. Sheffield, MA Matthew Wong, South Pasadena Middle School, South Pas., CA Alex Smyrnos. Rye Junior High, Rye, NH John Song. White Station High School, Memphis, TN Katie Miller. Dartmouth High School Max White. South Pasadena Middle School, South Pasadena, CA Haley Lewandowski. Fern Hill Elementary School, West Chester, PA Mallory Estopinal. Creekwood Middle School, Kingwood, TX Molly Hubbard. Creekwood Middle School, Kingwood, TX Daniel Pyon. South Pasadena Middle School, South Pasadena, CA Amanda Tu. Southridge School, BC, Canada Jeffrey Xiong. Arroyo Vista, South Pasadena, CA Hannah Szynal. Dartmouth High, Dartmouth, MA Caitlin Gray. Dartmouth High School, Dartmouth, MA Katherine Wang. South Pasadena Middle School, South Pasadena, CA Dan Dietz. Creekwood Middle School, Kingwood, TX Jennifer Saum. VCC, Kissimmee, FL Luong Anh. Carteret, NJ Luan Nguyen. Sheppard Middle School, San Jose, CA Kaitlyn Kassis. Marina Village Middle School Adria Leduc. Southridge School, Surrey, BC Kate Mittermaier. Southridge School, South Surrey, British Columbia John Lee. Southridge School. Surrey, BC Canada Anhang Zhu. Homestead High School, Cupertino, CA Sam Rosenberg. Monta Vista High School CA Nikki Tan. Southridge, Surrey BC Canada Sam Rosenberg. Monta Vista High School, Cupertino, CA Goulas Dimitris. NBG, Larissa, Greece Harry Siebert. Infineon, Munich, Germany Dave P. International School of Uganda Brian Chan. Summit Middle, Coquitlam, BC, Canada Luan Nguyen. Sheppard Middle School, San Jose, CA Bar Greengrass. Israel Diane Kristiansen. Westwood College, Dallas, TX Seong-Ho Lee. Saigon South International School, Ho Chi Minh, Vietnam Genoa Warner.  Dartmouth High School, Dartmouth, MA. Kevin Temew. Davao Christian High School, Davao City, Philippines Patrick Mc Henry. Gloucester City, NJ Pascale Philpot. Valencia community College, Kissimmee, FL Rahul Rege. Carwise Middle School, Palm Harbor, FL Rufus Hallam. Canterbury, England Melissa Chaffin. University of Georgia, Athens, GA Becky Britton. St. Luke Middle School, Columbus, GA Meagan Raposo. Dartmouth High, Dartmouth, MA Chris Hanes. West Port High School, Ocala, FL Gregory Loden. Lawrence School, Brookline, MA Keeyan. Roosevelt Elementary, Keego Harbor, MI Hirsh. Roosevelt Elementary, Keego Harbor, MI Zaaahid. Roosevelt Elementary, Keego Harbor, MI Jenna Custodio. Dartmouth High School, Dartmouth, MA Anna Wilson. Trinity High School, River Forest, IL Katie Grunow. Trinity High School, River Forest, IL Chloe London. Gladstone, OR Daniel Rodriguez. Tulsa Webster High School, Tulsa, OK Jamie Rochester. Tulsa Webster High School, Tulsa, OK John Segura. Dartmouth High School, South Dartmouth, MA Phillip Ai.  Hammarskjold Middle School, East Brunswick, NJ Jenna Turchanski. Holy Angels School, Calgary, Canada Rebecca Smith. Holy Angels School, Calgary, Canada Melinda Torrey. Osceola Middle School in Ocala, FL Tejal Patel. Carteret High School, Carteret, NJ Albert Zhou.  Scott Middle School, Lincoln, NE Sarah Maldonado. Creekwood Middle School, Kingwood, TX Caroline Brander. Trinity High School, River Forest, IL Paul Muiznieks. Chelmsford High School, Chelmsford, MA Crystal Koo. Steveston Secondary School, Richmond, B.C., Canada Catherine Cunningham. Creekwood Middle School, Kingwood, TX Tiffany Chen. South Pasadena Middle School, South Pasadena, CA Annabel Otero. Valencia Community College, Kissimmee, FL Carolyn Merchant. Dartmouth High School, Dartmouth, MA L. Morgan. Memphis, TN Ishwantie Braun. Valencia Community College, Kissimmee, FL Marty Hu. Palo Alto High School, Palo Alto, CA Joe Bao. Boulan Park Middle School, Troy, MI Sam Hemphill. Cong Tian. Sachem North High School, Long Island, NY Katherine Wang. South Pasadena Middle School, South Pasadena, CA Josh Andrews, Chelmsford High School, Chelmsford, MA Sarah Bartley. Rye Junior High School, Rye, NH Congyue Sukthose. Moogra School, Palo Alto, CA Chiraag Gupta. Southridge School, Surrey, B.C., Canada Leong HoongHan. Bukit Mertajam, Pulau Pinang, Malaysia. Andrew Economou. Carusi, Cherry Hill, NJ Nicholas Economou. Carusi, Cherry Hill, NJ Theja Lanka. Plano East Senior High, Plano, TX Jake Killian. Laguna Beach High School, Laguna Beach, CA Theja Lanka. Plano East Senior High, Plano, TX Cara Ong. Singapore Tina Wu. Berkley Street School, New Milfor, NJ Michael Necula. Laguna Beach High School, Laguna Beach, CA James Kawakami. South Pasadena Middle School, South Pasadena, CA Katherine Wang. South Pasadena Middle School, South Pasadena, CA Jay Malone. University of Oklahoma Health Science Center, Oklahoma City, OK Freddy Tsao. South Pasadena Middle School, South Pasadena, CA Matthew Wong. South Pasadena Middle School, South Pasadena, CA Karina Shaw. Laguna Beach High School, Newport Beach, CA Yoori Yang. Southridge School, Surrey, B.C, Canada Hannah Szynal. Darmouth High, Dartmouth, MA Lorena DoNascimento. Leominster High School, Leominster, MA Aaron Foreman. Creekwood Middle School, Kingwood, TX Masaki Norton. Lawrence School, Brookline, MA Alex Droznin. Lawrence School, Brookline, MA Jared Kulmatyski. R.F. Staples, Westlock, AB Yu Sakai.  Lawrence School, Brookline, MA Rafael Zambrano. Barranquilla, Colombia, SA David Friedman. Sippican Elementary, Marion, MA Qistina Hullon. Harmon Middle School, Aurora, OH Cray Math Project. New Castle, PA Christopher Sinkule. St.Luke Middle School, Columbus, GA Michael Belmonte. Carusi Middle School, NJ Anil Nataraj. Brookstone School, Columbus GA Michael Belmonte. Carusi, NJ Ashley Oxner. Richton, MS Kelly Galvin. Rye Junior High School, Rye, NH Sherif Rofael. Vodafone Academy, Cairo, Egypt Kelsey Finnell. White Station High School, Memphis, TN Mason Bates. Creekwood Middle School, Kingwood, TX Annelise Broussarid. Creekwood Middle School, Kingwood, TX Steve Lees. Arrowhead Union High School, Hartland, WI Britney White. Brookstone School, Columbus, GA Navdeep Johal. Carteret High School, Carteret, NJ Shengzhi Li. Shrewsbury High School, Shrewsbury, MA Jack Laubacher. Aurora, OH Rin Sone. South Pasadena Middle School, CA McKenzie Pieper. Creekwood Middle School Matt Welsh.  Arrowhead High School, Hartland, WI Nancy Huynh. MVRCS Upper School, Everett, MA Wendy Resch. Valencia Community College, Kissimmee, FL Amanda Frankwick. Arrowhead High School, WI Mary Smith, VCC, Kissimmee FL Brian Chester. Hartland, WI Alexandra Poli. Longfellow Middle School, Wauwatosa, WI Nicole Milad. Rye Junior High School, Rye, NH Lauren Frazier. Creekwood Middle School, Kingwood, TX Josh Henkel. Arrowhead High School, Hartland, WI Jonathan Hsu. Erin Sullivan. Aurora Harmon Middle School, Aurora, OH Stephen Pynenburg. Our Lady of Sorrows Catholic School, Toronto, Ontario Renae Shippy. Crest Ridge R-VII, Centerview, MO Chris McLachlan. Crocus Plains School, Brandon, Manitoba, Canada Matt Berry. Clinton Jr. High, Clinton, AR Alexander Kwok, South Pasadena Middle School, CA Avi Dhaliwal. Southridge Secondary School, Surrey, BC, Canada Rachel Oxner.  Richton High. Richton, MS Tabatha Shipley. Challenger Middle School Angela Shapiro. Valencia Community College, Orlando, FL Chris Livengood. Crest Ridge R-VII, Centerview, MO Roman Zyla. Our Lady of Sorrows, Toronto, Ontario Canada ThuyTrand Dinh. Sheppard Middle School, CA Pamela Schweit. Simi Valley High School, Simi Valley, CA. Lorna Ferguson. Chelmsford High School, Chelmsford, MA Samuel Coy. Farragut High School, IA Danny Gordon. Columbus, GA Robin Hammond. Pontiac Northern High School, Pontiac, MI Jenna Klein. Marina Village Middle School, El Dorado Hills, CA Allamanis Miltiadis. Anatolia High School, Thessaloniki, Greece Shura Watson. VCC. Kissimmee, FL. Max Pfenning. Harmon, Aurora OH Jennifer Sailor. Osceola Middle School, Ocala, FL Andrew Sailor. Osceola Middle School, Ocala, FL Shea Doonan. Hastings Middle School, Fairhaven, MA Mitchell Turner. Leesville Junior High, LA Roman Zyla. Our Lady of Sorrows, Toronto, Ont., Canada Cody Dunn.  South Pasadena Middle School, CA Ryan Elmer. Creekwood Middle School, Kingwood, TX Jassmyne Bretal. Hastings Middle School, Fairhaven, MA Kristin Ammon. Creekwood Middle School, Kingwood, TX Julie DeCorte, Canby High School, Canby, OR Alexander McAvoy. Hampshire Regional High School Mansi Raythatha. Creekwood Middle School, Kingwood, TX DeeDee Walker. St. Cloud, FL Elizabeth Brewer. Creekwood Middle School, Kingwood TX Lienn Swearingen. Parkersburg High School, Parkersburg WV John Burns. Carwise Middle School, Palm Harbor, FL Joseph Bergmeister. Creekwood Middle School, Kingwood, TX Panu Korpela. Naenae Intermediate, Lower Hutt, New Zealand Lienn Swearingen. Parkersburg High School, Parkersburg, WV Shannon Sattler. Hartland WI Jess Wrigley. Somerset College, Australia Eli Weinstein. South Pasadena Middle School, South Pasadena, CA Vishwas Chandra. White Station High School, Memphis, TN Jason Ku. Whitney High School, Cerritos, CA
	64% of respondents successfully answered this problem.

 

 Last Updated On: 11/16/05