Question

a company uses paper cups shaped like cones for its water cooler. each cup has a height of 12 cm, and the base has a radius of 5.5 cm. the cooler has 18,997 cm³ of water in it. how many cups can be filled from the cooler? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calcular volumen del cono

La fórmula del volumen de un cono es \( V = \frac{1}{3}\pi r^2 h \). Sustituimos \( r = 5.5 \), \( h = 12 \) y \( \pi = 3.14 \):
\( V = \frac{1}{3} \times 3.14 \times (5.5)^2 \times 12 \)
Calculamos \( (5.5)^2 = 30.25 \), luego:
\( V = \frac{1}{3} \times 3.14 \times 30.25 \times 12 \)
Simplificamos \( \frac{1}{3} \times 12 = 4 \), así:
\( V = 3.14 \times 30.25 \times 4 \)
\( 3.14 \times 30.25 = 94.985 \), luego \( 94.985 \times 4 = 379.94 \, \text{cm}^3 \).

Step2: Calcular número de copas

Dividimos el volumen total del refrigerador (\( 18997 \, \text{cm}^3 \)) por el volumen de una copa (\( 379.94 \, \text{cm}^3 \)):
\( \text{Número de copas} = \frac{18997}{379.94} \)
Calculamos: \( 18997 \div 379.94 = 50 \).

Answer:

50