Answer:
The volume of the softball is 6.6 times the volume of the tennis ball
Step-by-step explanation:
we know that
The volume of a sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
step 1
Find the volume of the softball
we have
[tex]r=3.75\ cm[/tex]
substitute
[tex]V=\frac{4}{3}(3.14)(3.75)^{3}=220.8\ cm^{3}[/tex]
step 2
Find the volume of the tennis ball
we have
[tex]r=2\ cm[/tex]
substitute
[tex]V=\frac{4}{3}(3.14)(2)^{3}=33.5\ cm^{3}[/tex]
step 3
Divide the volume of the softball by the volume of the tennis ball
[tex]220.8\ cm^{3}/33.5\ cm^{3}=6.6[/tex]
therefore
The volume of the softball is 6.6 times the volume of the tennis ball
Alternative Method
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
The scale factor is equal to the ratio of its radius
[tex]\frac{3.75}{2}=1.875[/tex]
therefore
The scale factor elevated to the cube is
[tex]1.875^{3}=6.6[/tex]
therefore
The volume of the softball is 6.6 times the volume of the tennis ball
