If you have ever taken a drive through farming areas, you have probably seen grain silos like the one above. These silos store grain for farmers. If you take the top of the silo off, you are left with a cylinder. Is there a way to find the surface area of a cylinder? Work through the tabs below to learn more.
Surface Area
Silo
The surface area of a cylinder is found with the same formula that we used for a prism. Think of a cylinder like a prism with curved sides. We can work through a few steps in order to find this formula.
| What is the perimeter of a circle called, and what is the formula for this perimeter? | The perimeter of a circle is called the circumference and is found with the equation C = 2πr. |
| How is the area of circle found? | Area of circle is found using the equation A = πr2. |
| We can start with our original equation for the surface area of a prism and then adapt it to fit a cylinder. Start with SA = 2B + ph and develop the formula for a cylinder. | SA = 2B + ph SA = 2(πr2) + 2πrh |
A silo at a local farm is 48 feet tall and has a diameter of 16 feet. What is the surface area of the silo? Round your answer to two decimal places.
The first thing we need to do is find the radius of the silo. We know that the diameter of the silo is 16 feet, so the radius is 8 feet, or half of the diameter.
| Next, we need to find the area of the base of the silo: | Area = πr2 Area = π(8)2 ≈ 201.06 ft2 |
| Next, we need to find the circumference of the silo. | C = 2πr = 2(π)(8) ≈ 50.27 ft |
| Now, let's use our surface area equation to finish the problem. | SA = 2(πr2) + 2πrh SA = 2(201.06) + 48(50.27) SA = 402.12 + 2412.96 SA = 2815.08 ft2 |
