1. Geometry 10-4 Cylinders

2. Definitions The lateral surface of a cylinder is the curved surface that connects the two bases. The (total) surface area of a cylinder is the curved surface plus the two bases. The bases of a cylinder are circles.

3. Formulas Lateral Surface Area S = 2πrh Total Surface Area S = 2πrh + 2πr 2 Volume V = Bh B = area of the base (circle = πr 2 )

4. Example Lena wants to cover a cylinder she found with colored paper to use as a storage container. The cylinder has a diameter of 16 inches and a height of 10 inches. How much paper will Lena need to decorate her container?

5. …continued Step 1 – Draw a picture Step 2 – Decide which formula you’ll use (what you’re looking for) Total Surface Area: S = 2πrh + 2πr 2

6. …continued Step 3 – Write out your variables r = 8, h = 10 Step 4 – Substitute the values S = 2π(8)(10) + 2π(8) 2 S = 2π(80) + 2π(64) S = 904.8 in 2

7. Example Find the lateral surface area of a marble container with a diameter of 11 cm and a height of 7 cm. 11 cm 7 cm

8. …continued Step 1 – Picture is given Step 2 – Formula Lateral surface area: S = 2πrh

9. …continued Step 3 – Variables r = 5.5, h = 7 Step 4 – Substitute S = 2π(5.5)(7) S = 241.9 cm 2

10. Example An oatmeal container is in the shape of a cylinder. The container has a height of 8 inches and a radius of 2 inches. How much oatmeal can the container hold?

11. …continued Step 1 – Draw a picture Step 2 – Choose your formula Volume: V = Bh 8 2

12. …continued Step 3 – Variables r = 2, h = 8 Step 4 – Substitute V = BhB = πr 2 V = π(2) 2 (8) V = 100.5 in 3