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dezoksy [38]
2 years ago
10

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.
Mathematics
1 answer:
madam [21]2 years ago
7 0

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.

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