Respuesta :
Q) We have a truck bed of 8ft x 5ft x 1.5ft, we want to know how many golf balls of 1.5 inches of diameter will fit in that bed.
A) In order to estimate how many golf balls will fit in the truck, we will make the following assumptions:
We will consider that the balls will perfectly fill all the volume of the bed of the truck. In real life that's not the case because when the balls are one over the other, we see that we have unfilled spaces between them.
1) First, we calculate the volume of the bed truck:
[tex]V_{\text{truck}}=8ft\cdot5ft\cdot1.5ft=60ft^3=60(12\cdot in)^3=103680in^3[/tex]Where we have taken into account that: 1 ft = 12 in.
2) Now we calculate the volume of each golf ball. We use the formula of volume of a sphere:
[tex]\begin{gathered} V_{\text{ball}}=\frac{4}{3}\cdot\pi\cdot R^3=\frac{4}{3}\cdot\pi\cdot(\frac{D}{2})^3=\frac{1}{6}\cdot\pi\cdot D^3 \\ V_{\text{ball}}=\frac{1}{6}\cdot\pi\cdot(1.5in)^3\cong1.767in^3 \end{gathered}[/tex]3) Finally, we calculate the number of balls that fit inside the bed of the truck dividing the volume of the bed by the volume of each ball:
[tex]N=\frac{V_{\text{truck}}}{V_{\text{ball}}}\cong\frac{103680in^3}{1.767in^3}\cong58777.589\cong60000[/tex]Answer
We see that approximately 60000 balls will fit inside the bed of the truck.
