# Rockefeller Center Christmas Tree – The ProblemsDecember 8, 2008

Facts:

Went up November 14, 2008
Illuminated December 3, 2008
Comes down January TBD, 2009

The first Rockefeller Center Christmas Tree was put up in 1931. The first Rockefeller Center Christmas Tree to be illuminated was in 1933.

The minimum size requirements: 65ft tall and 35 ft wide, though they like it to be 75-90 feet tall and proportionally wide.

Over 5 miles of lights are used to decorate the tree.

The 2008 tree was donated by a family from New Jersey. The tree was originally planted in 1931 by Mr. and Mrs. Varanyak and was the couple’s first Christmas tree. After planting it Mrs. Varanyak fertilized it religiously and said that it would end up in Rockefeller Center one day.

For the purposes of solving the following problems, let’s assume that the tree is a perfect cone.

This year’s tree measures 72 feet tall and 40 feet wide at its widest point. If the tree were cut down the middle from top to bottom, what would be the area of the cross-section?

What is the lateral height of the tree? Express your answer as a decimal to the nearest hundredth.
On the 5-mile long string of lights, there are 30,000 LEDs. If the lights are hung strictly on the surface of the tree and no lights are hung on the base, how many LEDs are there per sq foot of the tree’s surface area? Express your answer as a decimal to the nearest tenth.
Last year was the first year that Rockefeller Center’s tree went “green.” They installed 363 solar panels on the roof of the Rockefeller Center to off-set the power demands of the tree. They also used LEDs instead of standard lights. The LEDs alone reduced the tree’s energy consumption from 3510 kW/day to 1297 kW/day. What is the percent decrease in energy consumption seen due to the use of LEDs? Express your answer to the nearest whole number.

The solutions to this week's problems will be posted in the archive on Monday, December 15th, 2008.

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