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 reasoning. see example 1 on page 217 in the reference guide. a. 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.

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form is

Part b) The ratio of the volume of the smaller pyramid to the larger pyramid is

Part c) The volume of the smaller pyramid is

Step-by-step explanation:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

so

Let

z----> the scale factor

x----> the height of the smaller pyramid

y----> the height of the larger pyramid  

substitute the values

Simplify

-----> scale factor in simplest form

Part b) Ratio of the volume of the smaller pyramid to the larger pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid  

we have

substitute

Rewrite

-----> ratio of the volume of the smaller pyramid to the larger pyramid

Part c) The volume of the smaller pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid  

we have

substitute the values and solve for x

answer: ay  

fonsi  

dy  

oh

oh no, oh no

oh yeah

diridiri, dirididi daddy  

go

sí, sabes que ya llevo un rato mirándote  

tengo que bailar contigo hoy (dy)  

vi que tu mirada ya estaba llamándome  

muéstrame el camino que yo voy (oh)

tú, tú eres el imán y yo soy el metal  

me voy acercando y voy armando el plan  

solo con pensarlo se acelera el pulso (oh yeah)

ya, ya me está gustando más de lo normal  

todos mis sentidos van pidiendo más  

esto hay que tomarlo sin ningún apuro

despacito  

quiero respirar tu cuello despacito  

deja que te diga cosas al oído  

para que te acuerdes si no estás conmigo

despacito  

quiero desnudarte a besos despacito  

firmo en las paredes de tu laberinto  

y hacer de tu cuerpo todo un manuscrito (sube, sube, sube)

(sube, sube)