Answer:
[tex]r = \frac{7}{6}[/tex]
Explanation:
Given
Shape: Sphere
[tex]Surface\ Area = 17\frac{1}{9}[/tex]
Required
Determine the radius (r)
A sphere's surface area of is calculated using:
[tex]Surface\ Area = 4\pi r^2[/tex]
Substitute value for Surface Area
[tex]17\frac{1}{9} = 4\pi r^2[/tex]
Convert fraction to improper number
[tex]\frac{154}{9} = 4\pi r^2[/tex]
Divide both sides by 4
[tex]\frac{154}{9*4} = \pi r^2[/tex]
[tex]\frac{77}{9*2} = \pi r^2[/tex]
[tex]\frac{77}{18} = \pi r^2[/tex]
Divide both sides by [tex]\pi[/tex]
[tex]\frac{77}{18} * \frac{1}{\pi} = r^2[/tex]
Take [tex]\pi[/tex] as [tex]\frac{22}{7}[/tex]
So, we have:
[tex]r^2 = \frac{77}{18} * \frac{7}{22}[/tex]
[tex]r^2 = \frac{7}{18} * \frac{7}{2}[/tex]
[tex]r^2 = \frac{49}{36}[/tex]
Take the square root of both sides
[tex]r = \sqrt{\frac{49}{36}}[/tex]
[tex]r = \frac{7}{6}[/tex] --- approximated
Hence, the radius of the sphere is 7/6 units
