Question

Amira decides to estimate the volume of an apple by modeling it as a sphere. She measures its circumference as 43.4 cm. Find the apples's volume in cubic centimeters. Round your answer to the nearest tenth if necessary.

Answer 1

The formula for the circumference of a circle (or a sphere) is $2\pi r$.
The formula the volume of a sphere is $\frac{4}{3}\pi r^3$.
Assuming 43.4 includes the pi, we can do the equation $43.4=2\pi r$
Solving the equation, we get $\frac{43.4}{2\pi } =r$

Substituting r into the formua for the volume of a sphere, we get $\frac{4}{3} *\pi *(\frac{43.4}{2\pi } )^3$
Solving the cube (probably with a calculator), we get $\frac{4}{3} *\pi *\frac{81746.504}{8\pi ^3}$

It is a bit messy, but we can simplify further by cancelling out the pi's, which leaves us with $\frac{4}{3} *\frac{81746.504}{8\pi ^2}$.
With the butterfly method (or whatever you may call it), we can cancel out the 4 in the numerator and the 8 in the denominator, and multiply the 3 in the denominators.
Which gets us this: $\frac{81746.504}{6\pi ^2}$
Using a calculator, we get our final answer of (about) 1380.44cm^3

This was very messy, I apologize if I did make any mistakes.