Use the formula for volume of a sphere to find the volume of the hemisphere.
20 0003π ≈ 20 944 ft^3
Practice makes perfect
We want to find the volume of a silo which is shaped as a cylinder with a hemisphere attached at one end. Keep in mind that the length of the radius of a circle can be found by dividing the diameter by 2.
We will first find the volume of the cylinder and then the volume of the hemisphere. We will then add the results to find the volume of the silo. Let's do it!
Volume of the Cylinder
Let's begin by finding the volume of the cylinder.
The volume of a cylinder is the product of the area of the base and the height.
V= Bh
Our cylinder has a circular base, B, and its area is the product of π times the radius squared.
V= Bh ⇒ V = π r^2 h
Let's substitute the corresponding values into the formula and find its volume.
The top section of the silo is in the shape of a hemisphere.
The volume of a hemisphere is half the volume of a sphere.
V=43π r^3/2 ⇒ V = 2/3π r^3
We can now find the volume our hemisphere, which has a radius of 10 feet.
To find the volume of the composite solid we will use the Volume Addition Postulate.
The volume of a solid is the sum of the volumes of all its non-overlapping parts.
The solid has two non-overlapping parts, one cylinder and one hemisphere. Let's add their volumes.
V_(solid)= V_(cylinder)+ V_(hemisphere)
⇓
V_(solid)= 6000π+ 2000/3π = 20 000/3π
The solid has the volume 20 0003π ≈ 20 944 ft^3.
