Amber is purchasing a ring that has a 7.5 millimeter round pearl. Find the volume of the pearl to the nearest tenth.
+9466 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.
\(V = \frac43\pi(3.75/\pi)^3 \\~\\ V = \frac{4\pi*3375}{3*\pi^3*64} \\~\\ V = \frac{1125}{16\pi^2}\approx7.124\)
