To find the total volume of the grain silo, we need to calculate the volume of both the cylindrical portion and the hemispherical portion separately and then add them together.
1. Volume of the cylindrical portion:
V_cylinder = πr^2h
where r is the radius of the cylinder (10 feet) and h is the height of the cylindrical portion (30 feet).
V_cylinder = π(10)^2(30)
V_cylinder = π(100)(30)
V_cylinder = 3000π cubic feet
2. Volume of the hemispherical portion:
The volume of a hemisphere is given by
V_hemisphere = (2/3)πr^3
where r is the radius of the hemisphere, which is the same as the radius of the cylinder (10 feet).
V_hemisphere = (2/3)π(10)^3
V_hemisphere = (2/3)π(1000)
V_hemisphere = 666.67π cubic feet
3. Total volume of the grain silo:
Total volume = Volume of cylindrical portion + Volume of hemispherical portion
Total volume = 3000π + 666.67π
Total volume = 3666.67π cubic feet
Therefore, the total volume of the grain silo is 3666.67π cubic feet.
A grain silo is a cylinder with a hemisphere on top. In the Happy Farms grain silo, the height of the cylindrical portion is 30 feet. The radius is 10 feet. The volume of a cylinder is given by V = πr2h.What is the total volume of the grain silo? Explain how you found your answer.
1 answer