Option B is correct. [tex]V_T=\ \pi (2)^2(8.5)+\frac{1}{3} \pi (2)^2(13-8.5)\\[/tex]
The storage bin is constructed using a cylinder and a cone. Hence the total volume of the grain can be calculated using the formula;
[tex]V_T=V_C+V_{co}[/tex]
Vc is the volume of the cylinder
Vco is the volume of the cone.
For the cylinder:
Height of the cylinder hc = 8.5ft
radius rc = 4/2 = 2ft
[tex]V_c=\pi r_c^2h_c\\V_c=\pi(2)^2(8.5)[/tex]
For the cone:
Height of the cone = (13 - 8.5)ft
radius of the cone = radius of the cylinder rco = 2ft
[tex]V_{co}=\frac{1}{3} \pi r_{co}^2h_{co}\\ V_{co}=\frac{1}{3} \pi (2)^2(13-8.5)\\[/tex]
Taking the sum of the volumes;
[tex]V_T=\ \pi (2)^2(8.5)+\frac{1}{3} \pi (2)^2(13-8.5)\\[/tex]
This shows that option B is correct.
Learn more about the volume of composite objects here: https://brainly.com/question/14204462
