The Reunion Tower is one of the most recognizable landmarks in Dallas, Texas due to the giant sphere that sits atop the structure. The sphere, which houses observation decks accessible to visitors, has a diameter of 118 feet. Which value is closest to the volume of the dome? Use 3.14 for π.A. 859,852ft^3B. 1,679,406ft^3C. 2,350,879ft^3D. 2,510,782ft^3

Accepted Solution

The volume of a sphere uses the following formula:

[tex]V = \frac{4}{3}\pi r^{3}[/tex]

Because the question asks to use 3.14 in place of pi, the formula will now look like this:

[tex]V = (\frac{4}{3})(3.14)r^{3} = 4.18\overline{66} r^{3}[/tex]

We are given a diameter of 118 feet. The radius is half of the diameter, so divide the diameter by 2 to find the radius:

[tex]118 \div 2 = 59[/tex]
[tex]r = 59[/tex]

Plug this value into the formula, and solve with a calculator:

[tex]4.18\overline{66} \times 59^3 = 4.18\overline{66} \times 205379 = 859853.413[/tex]

Although our result is one cubic foot off, the answer is A. 859,852ft^3.

(859,852 is the result if the constant in the given formula is 4.18666, but the result with infinitely repeating numbers is 859,853.)