Question

a trucking company needs to move a pile of sand. the sand is stored in a pile shaped like a cone. the pile is 9 yards high, and its base has a radius of 5 yards. how many truckloads will the company need, if each truck holds 4.71 yd³ of sand? use 3.14 for π, and do not round your answer. truckloads

Explanation:

Step1: Calcular volumen del cono

La fórmula del volumen de un cono es \( V = \frac{1}{3}\pi r^2 h \). Dado \( r = 5 \) yd, \( h = 9 \) yd, \( \pi = 3.14 \). Sustituimos:
\( V = \frac{1}{3} \times 3.14 \times 5^2 \times 9 \)
\( 5^2 = 25 \), entonces \( V = \frac{1}{3} \times 3.14 \times 25 \times 9 \)
\( \frac{1}{3} \times 9 = 3 \), así que \( V = 3.14 \times 25 \times 3 \)
\( 3.14 \times 25 = 78.5 \), luego \( 78.5 \times 3 = 235.5 \) yd³.

Step2: Calcular número de camiones

Cada camión lleva \( 4.71 \) yd³. Dividimos el volumen total por la capacidad del camión:
\( \text{Número de camiones} = \frac{235.5}{4.71} \)
\( 235.5 \div 4.71 = 50 \).

Answer:

50