Answer:
Diamonds is incorrect, because, the volume of the softball is 8 times the volume of the golf ball
Step-by-step explanation:
we know that
The volume of a sphere is equal to
![V=\frac{4}{3}\pi r^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E%7B3%7D)
where
r is the radius
step 1
Find the volume of the golf ball
we have
![r=2.1\ cm\\pi =3.14](https://tex.z-dn.net/?f=r%3D2.1%5C%20cm%5C%5Cpi%20%3D3.14)
substitute
![V=\frac{4}{3}(3.14)(2.1)^{3}=38.77\ cm^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%283.14%29%282.1%29%5E%7B3%7D%3D38.77%5C%20cm%5E3)
step 2
Find the volume of the the softball
we have
![r=4.2\ cm\\pi =3.14](https://tex.z-dn.net/?f=r%3D4.2%5C%20cm%5C%5Cpi%20%3D3.14)
substitute
![V=\frac{4}{3}(3.14)(4.2)^{3}=310.18\ cm^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%283.14%29%284.2%29%5E%7B3%7D%3D310.18%5C%20cm%5E3)
step 3
Find the ratio of volumes
Divide the volume of the softball by the volume of the golf ball
![\frac{310.18}{38.77}=8](https://tex.z-dn.net/?f=%5Cfrac%7B310.18%7D%7B38.77%7D%3D8)
That means
Diamonds is incorrect, because, the volume of the softball is 8 times the volume of the golf ball