Question

#2
a cylindrical cup is 8 centimeters in height. when filled to the very top, it holds approximately 480 cubic centimeters of water. what is the radius of the cup, rounded to the nearest tenth?
show all your work.

standard: gmd.a.3
a food company is designing containers for several products.
each container is a cylinder. the company makes a single serving oatmeal container that holds 1.2 ounces oatmeal. they plan to make an extra large container for school cafeterias. the extra large container will be a dilation of the single serving container using a scale factor of 4. how many ounces of oatmeal will the extra large container hold? show all your work.
standard: gmd.a

Explanation:

Problema 1: Radio de la taza cilíndrica

Step1: Escribir fórmula del volumen

El volumen de un cilindro es $V = \pi r^2 h$

Step2: Sustituir valores conocidos

$480 = \pi r^2 (8)$

Step3: Despejar $r^2$

$r^2 = \frac{480}{8\pi} = \frac{60}{\pi}$

Step4: Calcular $r$ y redondear

$r = \sqrt{\frac{60}{\pi}} \approx \sqrt{19.0986} \approx 4.4$

Problema 2: Capacidad del recipiente ampliada

Step1: Relación de volúmenes por factor de escala

Al dilatar con factor $k$, el volumen se multiplica por $k^3$

Step2: Calcular factor de volumen

$k^3 = 4^3 = 64$

Step3: Calcular capacidad final

$1.2 \times 64 = 76.8$

Answer:

1. El radio de la taza es aproximadamente 4.4 centímetros.
2. El recipiente extra grande contendrá 76.8 onzas de avena.