Ch 12.3 S = Ph + 2B = (2π)(1.25) × (5) + 2(π)( ) = π L = Ph = (2π)(5) × (4) = 40π Find the lateral area of the cylinder. Find the surface area of the cylinder. Find the surface area of the prism. S = Ph + 2B = (4×6)(5) + 2(3)[(4×6)]/2 = 192 3

Ch 12.3 Volumes of Prisms & Cylinders Standard 9.0 Students compute the volumes of prisms and cylinders and commit to memory the formulas for prisms and cylinders. Learning Target: I will be able to solve problems involving volumes of prisms and cylinders. Ch 10.5 Ch 12.3

Concept Theorem 12-5 Ch 10.5 Ch 12.3

Example 1 Volume of a Prism Answer: The volume of the prism is 1500 cubic cm. V BhVolume of a prism 1500Simplify. Find the volume of the prism. Ch 10.5 Ch 12.3

Example 1 A.6480 in 3 B.8100 in 3 C.3240 in 3 D.4050 in 3 Find the volume of the prism. Ch 10.5 Ch 12.3 Volume of a prism B = (18×a)/2, a = √(30 2 – 18 2 ), h = 15 Multiply. = (216) (15) = 3240 V = Bh

Concept Ch 10.5 Ch 12.3 Theorem 12-6

Example 2 Volume of a Cylinder Find the volume of the cylinder in terms of π. Answer: The volume is approximately 18.3 cm 3. B = π r 2 =5.832πSimplify. = (1.8) 2 (1.8)r = 1.8 and h = 1.8 Ch 10.5 Ch 12.3 Volume of a cylinder V = Bh

Example 2 A.20π cm 3 B.200π cm 3 C.40π cm 3 D.320π cm 3 Find the volume of the cylinder in terms of π. Ch 10.5 Ch 12.3 Volume of a prism B = π r 2, r = 8, h = 5 Multiply. = π (8 2 ) (5) = 320π V = Bh

Concept Ch 10.5 Ch 12.3

Example 3 Volume of an Oblique Solid Find the volume of the oblique cylinder in terms of π. To find the volume, use the formula for a right cylinder. Answer: The volume is approximately 17,671.5 feet 3. B = π r 2 r 15, h 25 Ch 10.5 Ch 12.3 Volume of a cylinder V = Bh = 5625π Multiply.

Example 3 A.484π cm 3 B.5322π cm 3 C.1694π cm 3 D.2661π cm 3 Find the volume of the oblique cylinder to the nearest tenth. Ch 10.5 Ch 12.3 Volume of a cylinder B = π r 2, r = 11, h = 44 Multiply. = π (11 2 ) (44) = 5322π V = Bh

Example 4 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 APrism B Ch 10.5 Ch 12.3

Example 4 Read the Test Item You know the volume of each solid and that the difference between their volumes is 128 cubic inches. Solve the Test Item V B – V A = 128Difference of Volumes (4x ● 9) – (4x ● 5)=128Use V = Bh. 16x=128Simplify. x=8Divide each side by 16. Answer: The length of each prism is 8 inches. Ch 10.5 Ch 12.3 Prism APrism B

Example 4 A.4 in. B.6 in. C.8 in. D.10.5 in. 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? Prism A Prism B Ch 10.5 Ch 12.3 V B - V A = V difference V B – V A = 128 Difference of Volumes (6x ● 7) – (6x ● 11) = 192Use V = Bh. 24x = 192Simplify. x = 8