Lesson 11.3 Cylinders pp. 471-474.

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Lesson 9-3: Cylinders and Cones

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Presentation transcript:

Lesson 11.3 Cylinders pp. 471-474

Objectives: 1. To derive the formula for the volume of a cylinder. 2. To apply the formula to specific cylinders.

Theorem 11.4 The volume of a cylinder is the product of the area of a base and the height: V = BH. In particular, for a circular cylinder V = r2H.

EXAMPLE Find the volume. 12 5 V = r2H V = (5)2(12) V = 300 V ≈ 942.5 in3

Practice: Find the volume. Assume the base is circular. C = 24 in 16 in C = 2r 24 = 2r r = 12

Practice: Find the volume. Assume the base is circular. C = 24 in 16 in V = r2H V = (12)2(16) V = 2304 V  7238.2 in3

Practice: Find the volume. Assume the base is circular. 2 mm 4 cm d = 4 cm r = 2 cm r = 20 mm V = r2H V = (20)2(2) V = 800 V ≈ 2513.3 mm3

Homework pp. 472-474

Find the volume of each cylinder. 1. ►A. Exercises Find the volume of each cylinder. 1. 7 9

Find the volume of each cylinder. 5. ►A. Exercises Find the volume of each cylinder. 5. 11 19

►A. Exercises 9. A cylinder is lodged inside a square prism similar to the figure shown. How many inches are within the prism but outside the cylinder?

►A. Exercises 9. Vprism = BH = 182(26) = 8424 Vcylinder = BH = 182(26) = 8424 Vcylinder = BH = (92)(26) = 2106 V = Vp – Vc = 8424 - 2106 ≈ 1807.8 un3 9 26

►B. Exercises 11. The circumference of a cylinder is 86 meters, and the height is 63 meters. Find the surface area and volume of the cylinder. C = 2r 86 = 2r 43 = r

►B. Exercises 11. The circumference of a cylinder is 86 meters, and the height is 63 meters. Find the surface area and volume of the cylinder. V = BH B = r2 = 432 = 1849 V = 1849(63) = 116,487 m3

►B. Exercises 11. The circumference of a cylinder is 86 meters, and the height is 63 meters. Find the surface area and volume of the cylinder. S = L + 2B L = cH = 86(63) = 5418 S = 5418 + 2(1849) = 9116 m2

►B. Exercises 13. A cylindrical piece of iron has a diameter of 2 inches and a length of 16 inches. If it is melted down and poured into a rectangular mold that has a 1-by-3 base, what will be the length of the rectangular piece of iron?

►B. Exercises 15. How many cubic yards of concrete are needed to pour the patio and sidewalk if the thickness is to be four inches?

Patio 6’ 10’ 8’ 3’ 24’ ►B. Exercises 15.

■ Cumulative Review 25. circular cylinder Identify the horizontal cross section for each of the following figures. 25. circular cylinder

■ Cumulative Review 26. parallelepiped Identify the horizontal cross section for each of the following figures. 26. parallelepiped

■ Cumulative Review 27. tetrahedron Identify the horizontal cross section for each of the following figures. 27. tetrahedron

■ Cumulative Review 28. circular cone Identify the horizontal cross section for each of the following figures. 28. circular cone

■ Cumulative Review 29. sphere Identify the horizontal cross section for each of the following figures. 29. sphere