MATH SOLVE

3 months ago

Q:
# The radius of a softball is 3.75 cm, and the radius of a table tennis ball is 2 cm. The volume of the softball is how many times greater than the volume of the table tennis ball? show your work using radius. use 3.14 for pi. round to the nearest tenth

Accepted Solution

A:

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