the radius of a spare whose surface area is 17 whole one over nine​

Answers

Answer 1

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


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