Question

every year on december 31, cities celebrate the coming of the new year in different ways.
one popular way is to \drop\ a giant ball. the table below shows the dimensions of new
years balls used in some united states cities.

what is the mean volume of the new years balls given in the table?
round your answer to the nearest tenth.
cubic feet
submit

Explanation:

Step1: Calculate the volume of each ball

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^{3}\).

• For New York City (\(r = 6\)):

\(V_1=\frac{4}{3}\pi(6)^{3}=\frac{4}{3}\pi\times216 = 288\pi\)

• For Hilton Head Island (\(r = 4.5\)):

\(V_2=\frac{4}{3}\pi(4.5)^{3}=\frac{4}{3}\pi\times91.125=121.5\pi\)

• For Panama City (\(r = 5\)):

\(V_3=\frac{4}{3}\pi(5)^{3}=\frac{4}{3}\pi\times125=\frac{500}{3}\pi\)

Step2: Calculate the mean volume

The mean formula is \(\bar{V}=\frac{V_1 + V_2+V_3}{3}\).
Substitute \(V_1 = 288\pi\), \(V_2=121.5\pi\), \(V_3=\frac{500}{3}\pi\) into the formula:

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Take \(\pi\approx3.14\), then \(\bar{V}=\frac{1728.5\times3.14}{9}\approx\frac{5427.49}{9}\approx603.0544\approx603.1\)

Answer:

\(603.1\)