Question

a company uses paper cups shaped like cones for its water cooler. each cup has a height of 8 cm, and the base has a radius of 3 cm. how much water is needed to fill 225 cups? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calcular volumen de un cono

La fórmula del volumen de un cono es \( V = \frac{1}{3}\pi r^2 h \). Dado \( r = 3 \, \text{cm} \), \( h = 8 \, \text{cm} \) y \( \pi = 3.14 \). Sustituimos:
\( V = \frac{1}{3} \times 3.14 \times 3^2 \times 8 \)
\( 3^2 = 9 \), entonces \( V = \frac{1}{3} \times 3.14 \times 9 \times 8 \)
\( \frac{1}{3} \times 9 = 3 \), así que \( V = 3.14 \times 3 \times 8 = 75.36 \, \text{cm}^3 \) (volumen de un vaso).

Step2: Volumen total para 225 vasos

Multiplicamos el volumen de un vaso por 225:
\( V_{\text{total}} = 75.36 \times 225 \)
\( 75.36 \times 225 = 16956 \)

Answer:

16956