Lección 11
Llenar recipientes
Llenemos un recipiente con agua.
Problema 1
Los cilindros A, B y C tienen el mismo radio pero diferentes alturas. Coloca los cilindros en orden de acuerdo a su volumen, del menor al mayor.
![Three cylinders, A, B and C. No dimensions are given. Cylinder A is taller than Cylinder B. Cylinder C is taller than Cylinder B, and not as tall as Cylinder A](https://staging-cms-im.s3.amazonaws.com/wFQg6tkoFLCybDryK137sc7e?response-content-disposition=inline%3B%20filename%3D%228-8.5.NewPP.Cylinders354.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.NewPP.Cylinders354.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141700Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=83a5b4ef9cceb96f4f6d94f1af78d7fa5616b7ecef5c222c64594cca147b44bd)
Problema 2
Dos cilindros, \(P\) y \(Q\), comenzaron cada uno con distintas cantidades de agua. La gráfica muestra cómo cambió la altura del agua a medida que el volumen del agua aumentó en cada cilindro. Empareja las gráficas de \(a\) y \(b\) a los cilindros P y Q. Explica tu razonamiento.
![](https://staging-cms-im.s3.amazonaws.com/SV33zRuSSUDM8djqbS7GJ2ME?response-content-disposition=inline%3B%20filename%3D%228.5.D11.Image.Revision.113_es.png%22%3B%20filename%2A%3DUTF-8%27%278.5.D11.Image.Revision.113_es.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141700Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=bbfad4f057932b55547759cbc84bcdcb296d59885ff50b9552b31aaf0b739edb)
![](https://lausd-ms-math.s3.amazonaws.com/uploads/pictures/8/8.5.NewPP.Cylinders13.png)
Problema 3
¿Cuál de las siguientes gráficas podría representar el volumen de agua en un cilindro como una función de su altura? Explica tu razonamiento.
![Three graphs, all quadrant 1. First, straight line, through origin, positive slope. Second, horizontal line begins above origin. Third, curve begins at origin, increases as it moves right.](https://staging-cms-im.s3.amazonaws.com/agpACcXtq3JPYWVqoxepz3W2?response-content-disposition=inline%3B%20filename%3D%228-8.5.NewPP.3graphs.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.NewPP.3graphs.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141700Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d4b7dfc0f8e3672a207d8059230579bc072b8589e3699db9a39de1ecfa5702d4)
Problema 4
La suma del área de los rectángulos es 30 centímetros cuadrados.
![Two rectangles. First, 3 centimeters by x centimeters. Second, y centimeters by 2 centimeters.](https://staging-cms-im.s3.amazonaws.com/EMecoiLubErUuYrh28cz5NU6?response-content-disposition=inline%3B%20filename%3D%228.5.B3.PP.Image.101.png%22%3B%20filename%2A%3DUTF-8%27%278.5.B3.PP.Image.101.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T141700Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5bc70f27834c47bed5bd32a42cc871dea1569d29e0d9bfc7c6bce25dda64ad10)
- Escribe una ecuación que muestre la relación entre \(x\) y \(y\).
- Completa la tabla con los valores que faltan.
\(x\) 3 8 12 \(y\) 5 10