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Amber is purchasing a ring that has a 7.5 millimeter round pearl. Find the volume of the pearl to the nearest tenth.

Guest Mar 22, 2017
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Pearls are sphere shaped, so we will use the formula for the volume of a sphere.

\(V = \frac43\pi r^3\)

 

The only question is what is r? What is the radius?

 

Well, the pearle is 7.5 mm round. I think this means that the circumference is 7.5 mm.

And

circumference = 2* π * radius

so

7.5 mm = 2* π * radius

7.5 mm / (2π) = radius

3.75/π mm= radius

 

Now we know the radius. Just plug this into the formula for the volume of a sphere.

\(V = \frac43\pi(3.75/\pi)^3 \\~\\ V = \frac{4\pi*3375}{3*\pi^3*64} \\~\\ V = \frac{1125}{16\pi^2}\approx7.124\)

hectictar  Mar 22, 2017

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