Question

(08.02 LC) A company that manufactures storage bins for grains made a drawing of a silo. The silo has a conical base, as shown below: The figure shows a silo shaped as a closed cylinder with a conical end. The diameter of the silo is 4 ft, the length of the cylindrical part is 10 ft, and the entire length of the silo is 13 ft. Which of the following could be used to calculate the total volume of grains that can be stored in the silo? (6 points) π(2ft)2(10ft) + one over three π(13ft − 10ft)2(2ft) π(10ft)2(2ft) + one over three π(13ft − 10ft)2(2ft) π(2ft)2(10ft) + one over three π(2ft)2(13ft − 10ft) π(10ft)2(2ft) + one over three π(2ft)2(13ft − 10ft)

Answer 1

Answer:

π(2ft)2(10ft) + one over three π(2ft)2(13ft − 10ft)

Explanation:

Given the following:

Diameter of silo = 4ft

Length of silo (h)= 13ft

Length of cylindrical part (h)= 10ft

Therefore, length of conical part(h) = (13 - 10) = 3ft

Radius(r) = diameter/2 = 4/2 = 2

The volume of a cylinder :

πr^2h

π(2ft)^210ft = π4ft10ft

The volume of cone :

1/3πr^2h

1/3π(2ft)^23ft = 1/3π4ft3ft

Therefore, the total volume of grains that can be stored in the silo equals

The volume of cylinder + volume of a cone

π(2ft)^210ft + 1/3π(2ft)^2(13 - 10)ft