Question

jessicas company makes solid metal balls for various industrial uses. a customer wants iron balls that have a diameter of 9 in. if jessica must make 30 of these balls, how much iron will she need? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Encontrar el radio de la esfera

El diámetro es 9 in, así que el radio \( r = \frac{9}{2} = 4.5 \) in.

Step2: Calcular el volumen de una esfera

La fórmula del volumen de una esfera es \( V = \frac{4}{3}\pi r^3 \). Sustituyendo \( r = 4.5 \) y \( \pi = 3.14 \):
\( V = \frac{4}{3} \times 3.14 \times (4.5)^3 \)
Primero, calcular \( (4.5)^3 = 4.5 \times 4.5 \times 4.5 = 91.125 \)
Luego, \( \frac{4}{3} \times 3.14 = \frac{12.56}{3} \approx 4.1867 \)
Entonces, \( V \approx 4.1867 \times 91.125 = 381.51 \) in³ (volumen de una esfera)

Step3: Calcular el volumen total para 30 esferas

Multiplicar el volumen de una esfera por 30: \( 381.51 \times 30 = 11445.3 \) in³

Answer:

11445.3