The height of one solid limestone square pyramid is 21 m. A similar solid limestone square pyramid has a height of 30 m. The volume of the larger pyramid is 12,000 m3. Determine each of the following, showing all your work and reasoninga. The scale factor of the smaller pyramid to the larger pyramid in simplest form. b. Ratio of the volume of the smaller pyramid to the larger. c. The volume of the smaller pyramid. Show your work and label your answer.

Answer:Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form is [tex]\frac{7}{10}[/tex]part b) The ratio of the volume of the smaller pyramid to the larger is [tex]\frac{343}{1,000}[/tex]Part c) The volume of the smaller pyramid is [tex]4,116\ m^{3}[/tex]Step-by-step explanation:Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest formwe know thatIf two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factorsoLetz----> the scale factorx----> the height of the smaller pyramidy----> the height of the larger pyramid   [tex]z=\frac{x}{y}[/tex]substitute the values[tex]z=\frac{21}{30}[/tex]Simplify[tex]z=\frac{7}{10}[/tex] ----> scale factor in simplest formPart b) Ratio of the volume of the smaller pyramid to the larger pyramidwe know thatIf two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cubesoLetz----> the scale factorx----> the volume of the smaller pyramidy----> the volume of the larger pyramid   [tex]z^{3}=\frac{x}{y}[/tex]we have[tex]z=\frac{7}{10}[/tex]substitute[tex](\frac{7}{10})^{3}=\frac{x}{y}[/tex][tex](\frac{343}{1,000})=\frac{x}{y}[/tex]Rewrite[tex]\frac{x}{y}=\frac{343}{1,000}[/tex] ----> ratio of the volume of the smaller pyramid to the largerPart c) The volume of the smaller pyramidwe know thatIf two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cubesoLetz----> the scale factorx----> the volume of the smaller pyramidy----> the volume of the larger pyramid   [tex]z^{3}=\frac{x}{y}[/tex]we have[tex]z=\frac{7}{10}[/tex][tex]y=12,000\ m^{3}[/tex]substitute[tex]\frac{7}{10}^{3}=\frac{x}{12,000}[/tex][tex]\frac{343}{1,000}=\frac{x}{12,000}[/tex][tex]x=12,000*343/1,000[/tex][tex]x=4,116\ m^{3}[/tex]