MATH SOLVE

3 months ago

Q:
# The volumes of two similar solids are 53 cm^3 and 1113 cm^3, which is the ratio of the corresponding sides? A) 21 B) 3β21 C) β21 D) 7

Accepted Solution

A:

Answer:The ratio of its corresponding sides is [tex]\sqrt[3]{21}[/tex]Step-by-step explanation:we know thatIf two solids are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor. And the ratio of its volumes is equal to the scale factor elevated to the cubeLetz ----> the scale factorx ----> the volume of the larger solidy ----> the volume of the smaller solidso[tex]z^{3}=\frac{x}{y}[/tex]we have[tex]x=1,113\ cm^{3}[/tex][tex]y=53\ cm^{3}[/tex]substitute[tex]z^{3}=\frac{1,113}{53}=21[/tex][tex]z=\sqrt[3]{21}[/tex]thereforeThe ratio of its corresponding sides is [tex]\sqrt[3]{21}[/tex]