Question

a manufacturer makes decorative globes out of silver in the shape of a solid sphere. suppose each sphere has a radius of 1.5 cm. if silver is priced at $6.00 per cm³, how much will the silver cost to make one solid sphere? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calcular el volumen de la esfera

La fórmula del volumen de una esfera es \( V = \frac{4}{3}\pi r^3 \). Dado \( r = 1.5 \, \text{cm} \) y \( \pi = 3.14 \):
\( V = \frac{4}{3} \times 3.14 \times (1.5)^3 \)
\( (1.5)^3 = 3.375 \)
\( V = \frac{4}{3} \times 3.14 \times 3.375 \)
\( \frac{4}{3} \times 3.375 = 4.5 \)
\( V = 3.14 \times 4.5 = 14.13 \, \text{cm}^3 \)

Step2: Calcular el costo del plata

El costo por \( \text{cm}^3 \) es \( \$6.00 \). Entonces, el costo total es \( \text{Volumen} \times \text{Costo por cm}^3 \):
\( \text{Costo} = 14.13 \times 6 = 84.78 \)

Answer:

\( \$84.78 \)