LESSON 12 4 Volumes of Prisms and Cylinders

LESSON 12– 4 Volumes of Prisms and Cylinders

Five-Minute Check (over Lesson 12– 3) TEKS Then/Now Key Concept : Volume of a Prism Example 1: Volume of a Prism Key Concept: Volume of a Cylinder Example 2: Volume of a Cylinder Key Concept: Cavalieri’s Principle Example 3: Volume of an Oblique Solid Example 4: Comparing Volumes of Solids

Over Lesson 12– 3 Find the surface area of the regular pyramid. A. 600 in 2 B. 623. 2 in 2 C. 635. 3 in 2 D. 647. 4 in 2

Over Lesson 12– 3 Find the surface area of the cone. A. 628. 3 ft 2 B. 642. 3 ft 2 C. 677. 8 ft 2 D. 753. 9 ft 2

Over Lesson 12– 3 Find the surface area of the regular pyramid. A. 420 ft 2 B. 480 ft 2 C. 679. 8 ft 2 D. 710 ft 2

Over Lesson 12– 3 Find the surface area of the cone. A. 214. 2 m 2 B. 221. 0 m 2 C. 233. 4 m 2 D. 247. 5 m 2

Over Lesson 12– 3 Find the surface area of a square pyramid with base length of 10 feet and slant height of 8 feet. A. 80 ft 2 B. 200 ft 2 C. 240 ft 2 D. 260 ft 2

Over Lesson 12– 3 Find the lateral area of a cone with a diameter length of 10 centimeters and a slant height of 13 centimeters. Round your answer to the nearest tenth. A. 204. 2 cm 2 B. 282. 7 cm 2 C. 408. 4 cm 2 D. 722. 6 cm 2

Targeted TEKS G. 10(B) Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change. G. 11(D) Apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure. Mathematical Processes G. 1(D), G. 1(E)

You found surface areas of prisms and cylinders. • Find volumes of prisms. • Find volumes of cylinders.

Volume of a Prism Find the volume of the prism. V Bh Volume of a prism 1500 Simplify. Answer: The volume of the prism is 1500 cubic centimeters.

Find the volume of the prism. A. 6480 in 3 B. 8100 in 3 C. 3240 in 3 D. 4050 in 3

Volume of a Cylinder Find the volume of the cylinder to the nearest tenth. Volume of a cylinder = (1. 8)2(1. 8) r = 1. 8 and h = 1. 8 ≈ 18. 3 Use a calculator. Answer: The volume is approximately 18. 3 cm 3.

Find the volume of the cylinder to the nearest tenth. A. 62. 8 cm 3 B. 628. 3 cm 3 C. 125. 7 cm 3 D. 1005. 3 cm 3

Volume of an Oblique Solid Find the volume of the oblique cylinder to the nearest tenth. To find the volume, use the formula for a right cylinder. Volume of a cylinder r 15, h 25 Use a calculator. Answer: The volume is approximately 17, 671. 5 cubic feet.

Find the volume of the oblique cylinder to the nearest tenth. A. 1520. 5 cm 3 B. 16, 725. 8 cm 3 C. 5324 cm 3 D. 8362. 9 cm 3

Comparing Volumes of Solids Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 128 cubic inches greater than the volume of Prism A, what is the length of each prism? Prism A Prism B A 12 B 8 C 4 D 3. 5

Comparing Volumes of Solids Read the Item You know the volume of each solid and that the difference between their volumes is 128 cubic inches. Solve the Item Volume of Prism B – Volume of Prism A = 128 Write an equation. 4 x ● 9 – 4 x ● 5 = 128 Use V = Bh. 16 x = 128 Simplify. x =8 Divide each side by 16. Answer: The length of each prism is 8 inches. The correct answer is B.

Prisms A and B have the same width and height, but different lengths. If the volume of Prism B is 192 cubic inches greater than the volume of Prism A, what is the length of each prism? A. 4 in. Prism A B. 6 in. C. 8 in. D. 10. 5 in. Prism B

LESSON 12– 4 Volumes of Prisms and Cylinders